Sam, who is gay, was selected by the St. Louis Rams in the seventh round of the May draft.
"I wouldn't have taken him," Dungy told the Tampa Tribune. "Not because I don't believe Michael Sam should have a chance to play, but I wouldn't want to deal with all of it. It's not going to be totally smooth ... things will happen."
Colts general manager Ryan Grigson said on the draft's final day that Indianapolis considered selecting Sam with one of their picks.
Sam's situation may end up being a distraction inside the locker room and for the franchise, but the Rams deserve credit for being willing to select him.
Coach Chuck Pagano and punter Pat McAfee were two of the many Colts who earlier this year said they would have no problem with Sam's orientation inside their locker room.
"I love the environment we've created, the culture we've created," Pagano said earlier this year. "I think we have an outstanding locker room. The Colts never have and never will discriminate based on sexual orientation. We look at the player. We'll evaluate him just like we evaluate everybody else. If he can help our team and help us win football games, he'll be more than welcome."