On ESPN's "Mike & Mike" on Monday, Pinkel recalled a team-building exercise in August that set the stage for Sam to reveal his sexual orientation to his teammates.
Periodically throughout the year, Pinkel said, each Missouri coach will invite about 15 players from different position units to his home for "cross-over dinners."
"They'll all come over, having dinner at my house, and I'll stand up and say, 'I'm Gary Pinkel, I'm from Akron, Ohio,' and I start talking about my family, everything about my family. And everybody unloads everything about themselves. It's remarkable."
Sam was at an assistant coach's house when he told his teammates he is gay.
"In August he was in another group, and I got a call from the coach right afterward that Michael told the whole group that he's gay," Pinkel said. "That's when I first heard of it."
Sam had already come out privately to wide receiver L'Damian Washington, who happened to be at Sam's dinner that night.
"I knew that something was about to come because of the way he was balling up the paper in his hands," Washington told the New York Times. "He kept rolling it up. So I kind of knew something was coming, but I didn't think it was that."
The next day, Pinkel asked Sam how he wanted to handle coming out to the rest of the world, asking him, "We have to talk about, 'Now what do you want to do? Do you want this to come out now? Do you want to after the season? After the NFL draft? What are you thinking here, Mike?'"
After discussing the ramifications of Sam's decision with the athletic department's public relations staff, Sam thought about it overnight before deciding to postpone any announcement until after the season, Pinkel said.
Pinkel said Sam told him, "I do not want to have any distractions for our football team. We've got to concentrate on football, and I'll [come out] at another time."
Sam said he was thrilled with the show of support within the program.
"Just to see their reaction was awesome," he told ESPN. "They supported me from day one. I couldn't have better teammates. ... I'm telling you what: I wouldn't have the strength to do this today if I didn't know how much support they'd given me this past semester."
Missouri tweeted a photo of Memorial Stadium from Monday where the letters "S" and "A" were etched out in the snow, to go with the M in a show of support for Sam.
Pinkel said no players came directly to the coaching staff with concerns after Sam revealed his sexual orientation to the team, but he suspects that there was initially a mixed reaction.
"There are certainly players that have differences of opinions, not only on this but other social issues," Pinkel said. "I'm not naive enough to believe that [there is not], I'm sure there are. But at the end of the day, it's about the team, it's about the family. We accept one another, we accept our differences, and that's where respect and understanding is important."
A respect of cultural differences is one of Missouri's four core values, Pinkel said, and he was proud of how his team stuck together after Sam came out.
"I'm really proud of Mike and really proud of our football team," Pinkel said. "We have great kids and good people, and they're understanding. That's kind of the environment we have and the family atmosphere at Mizzou."
Without the extra attention of being a publicly gay athlete, Sam had a standout season for the Tigers, leading the SEC with 19 tackles for a loss and 11.5 sacks, which tied the school's single-season record.
He was named co-defensive player of the year in the SEC and helped Missouri finish 7-1 in the conference, winning the SEC East division. He also forced a fumble on a sack late in the fourth quarter to secure Missouri's victory over Oklahoma State in the AT&T Cotton Bowl.
But throughout Sam's success, Missouri declined all interview requests for him during the season, multiple media outlets reported Monday. He finally spoke to reporters after the Cotton Bowl, saying he was focused on football and graduating and didn't want any outside distractions.
"I think that helped him a lot, because he was under pressure," Josey told the Star. "That comes with anybody that's hiding something, so I'm proud that he had the courage to come out -- and now to tell the world that he's gay and he's comfortable with it."
Sam came to Pinkel's office last week when it was time to make his announcement, saying he was aware that most people knew he was gay.
"I think one of the great things about Michael is that he wanted to tell his story," Pinkel said. "I told him this is going to be big, which is an understatement, but he's a great young man and I'm very, very proud of him."