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."