But he's not second-guessing how the team handled Tagovailoa throughout the week.
Tagovailoa was taken to a hospital Thursday after hitting his head on the turf while being sacked by Cincinnati Bengals nose tackle Josh Tupou in the second quarter. He remained on the turf for roughly 12 minutes before he was carted off the field on a stretcher and eventually taken to the University of Cincinnati Medical Center with a concussion and neck injury.
He was diagnosed with a concussion and is in the protocol with no timetable for a return, according to the Dolphins.
Tagovailoa took to Twitter to thank everyone for their support and said he's "feeling much better."
The injury occurred four days after a similar incident during Miami's game Sunday against the Buffalo Bills, in which Tagovailoa hit the back of his head on the ground and was evaluated for a concussion. The Dolphins faced widespread criticism on social media for allowing Tagovailoa to return to the game, as well as skepticism from the NFL Players Association -- which after Sunday's game, initiated its right to request a review of the NFL's concussion protocol.
"We are all outraged by what we have seen the last several days and scared for the safety of one of our brothers," Tretter said. "What everyone saw both Sunday and last night were 'no-go' symptoms within our concussion protocols. The protocols exist to protect the player and that is why we initiated an investigation.
"Our job as the NFLPA is to take every possible measure to get the facts and hold those responsible accountable. We need to figure out how and why the decisions were made last Sunday to allow a player with a 'no-go' symptom back on the field."
But the Dolphins say Tagovailoa passed multiple concussion evaluations -- including one at halftime of the Bills game and each day leading up to Thursday's game, according to NFL chief medical officer Allen Sills.
"I have 100 percent conviction in our process regarding our players," McDaniel said. "This is a player-friendly organization, and I make it very clear from the onset that my job here is for the players. I take that very seriously. No one in the building strays from that. ... If there would have been anything lingering with his head, I wouldn't have been able to live with myself if I prematurely put someone out there and put them in harm's way.
"This is a relationship that I have with this human being. I take that serious. I wouldn't have put him out there if there was any inclination given to me whatsoever that he was endangering himself from that previous game."
Contrary to Miami's previous game when Tagovailoa was taken directly to the locker room from the field, McDaniel had a chance to interact with his quarterback before he was stretchered off the field.
He said he knew essentially right away that Tagovailoa had a concussion and hoped that it wasn't anything more.
"Obviously, I was very worried about his head, but you're wanting to make sure that all things with relation to the spine and back and all that stuff, you want to make sure that's OK," McDaniel said. "It was very clear to me from the onset that he had, I didn't really the know the degree of, but I knew he had a concussion.
"He was asking for me and then when he saw me, I could just tell it wasn't the same guy that I'm used to seeing."
After the game, McDaniel told the team Tagovailoa would be traveling back to Miami with them. It was galvanizing news to a locker room that was somber beyond the scope of a normal loss.
"All of his teammates were so elated. I mean this was a scary, scary situation for all of us," McDaniel said. "I'm sure you could tell by his teammates' body language and everyone that was on the field. It was something that did not just go away once the game restarted. All of his teammates were absolutely elated to see him on the plane. He was elated. It brought him some joy, which was good to see. It's one of the reasons you get into team sports."
The Dolphins continue to face criticism for their handling of the 24-year-old, but McDaniel insists every step of the NFL's concussion protocol was followed.
He said he understands the optics of the entire situation but can speak with "100 percent conviction" that every person in the Dolphins' building adhered to a process that is "clear, contrite and not something that is negotiable in any way, shape or form."
"I had no worries whatsoever. I'm in steady communication with this guy day-in and day-out," McDaniel said Friday. "We're talking about high-level football conversations about progressions and defenses and recalling stuff from two weeks previous and then him having to reiterate a 15-word play call. All things, absolutely no signs. There was no medical indication, from all resources, that there was anything regarding the head.
"Beyond an eyeball test, which I know for a fact you guys would not be very comfortable if I was just relying on that -- I mean, it's the reason why we have tests. He did not have a head injury. So, guys hit their heads all the time, and that's why I was adamant [that] he was evaluated for having a head injury and he did not have one. And when I tell you he was in complete mental concert, talking to us through it, and then he played the whole game and then he did a press conference and then he did media all week.
"If I were to sit someone for a medical issue going against medical people abstractly, then when do I play him again?"
Veteran quarterback Teddy Bridgewater finished the game in Tagovailoa's place, and McDaniel confirmed Bridgewater will be the starter moving forward while Tagovailoa is out.
Seeing Tagovailoa leave Thursday's game was a tough sight for many around the league.
Coach John Harbaugh, whose Baltimore Ravens lost to the Dolphins in Week 2, said the whole situation was unbelievable.
"Like probably most people, I couldn't believe what I saw last night. I couldn't believe what I saw last Sunday. It was just something that was astonishing to see," Harbaugh said Friday. "I've been coaching for 40 years now, college in the NFL, almost 40, and I've never seen anything like it before. I just couldn't believe what I was seeing.
"A lot of times players want to play and sometimes you just have to tell them 'No. No has to be the answer.'"
"I think it's a scary moment for anybody to be in that type of disposition," Hurts said Friday.
McDaniel reiterated multiple times that he has not considered any sort of timetable when it comes to Tagovailoa's return. He said Tagovailoa underwent an MRI on Friday and that the team would take it day-by-day as far as what will be asked of him while in concussion protocol; if there is any indication that traveling to and from the facility isn't what's best for him, the Dolphins will not ask him to do so until it is.
"I literally have no timetable or even thought to it. That's where I would feel irresponsible is even thinking about it," he said. "I want him to get all the evaluations possible. I want him to do all the things recommended from all of the medical counterparts. And I want him to get on the road to recovery from that as a human being and then we'll cross that bridge. But in terms of a timeline of crossing that bridge, I have zero idea."