Mourinho’s side were beaten 4-1 by arch-rivals Liverpool in the International Champions Cup match.
The United boss revealed that Bailly wasn’t supposed to feature in the game but made the decision to come in and play when Chris Smalling withdrew from the side just before kick-off.
“Eric Bailly was injured – he shouldn’t be playing,” Mourinho said.
“But when he saw that Smalling in the warm-up was coming out, he made the decision by himself: ‘I’m not going to let my team play with five kids in the back against Salah, Mane and company’.
“So he put himself there for 90 minutes and now his ankle is [much worse].
“He was there for 90 minutes so I have some brave boys.”
Managers Jurgen Klopp and Mourinho have clashed in recent days over spending, and it was Klopp’s Reds who came out on top in Michigan with goals from Sadio Mane, Daniel Sturridge, Sheyi Ojo and Xherdan Shaqiri on debut.
Andreas Pereira scored a free-kick for United but could not stop Liverpool making it two wins from three in the tournament.
Mourinho added: “This is not a step for anything, the majority of the payers which played are not going to play.
“Some of them are not even going to belong to the squad.”
Next up for Manchester United is a friendly against Real Madrid on Wednesday.