Mourinho, having replaced Dutch gaffer Louis Van Gaal, limited Schweinsteiger's game time before sending him to the U23.
But the Portuguese trainer has accepted he was wrong for making a decision like that.
"I didn't play a lot [under Mourinho] unfortunately, but I still respect him. He's a great manager who has won a lot of trophies. It was a weird and difficult situation, he never really explained to me why," Schweinsteiger told BBC Radio 5 Live.
"At the end of the day, it is in the past, it's history. But I loved playing for United, the fans were absolutely amazing. I loved every single moment.
"In the first year under Louis van Gaal, until I got injured, when Leicester won the title, we were up there and battling for the first position.
"We were very successful, I think, even without big signings like Zlatan [Ibrahimovic] or Paul [Pogba]. We should have won much more with those big signings, except I couldn't play with them.
"It was maybe because I played under Pep Guardiola and had played Pep Guardiola football, which he doesn't like so much, I think. Still, I also liked how Mourinho was, actually, coaching.
"Of course the game style is different - I think that is why Zlatan left. It was not so much football, sometimes it was more direct. But he had success with his teams. It was just a strange feeling.
"I don't think it was his personal opinion. At the end of the day, he apologised to me and said it was a big mistake. It was just too late. The decision, I think, was made before he actually arrived."
