The 22-year-old Ivory Coast international started in central defence alongside Daley Blind as United commenced the Mourinho era with a piece of silverware courtesy of a 2-1 victory over the reigning Premier League champions.
"I think Bailly is the perfect opponent for people like they have because he is as fast as they are," he said on BT Sport and MUTV.
"I know the player he is but you always have a little question mark when a player comes from a completely different level and plays his first match for Manchester United officially at Wembley with these responsibilities, without (Chris) Smalling.
"The way he played I think he was really good but I have to say Daley also gave him the stability he needs."
Mourinho added: "Eric is working since day one, he started the pre-season with us, he played matches, he's fit so I knew that with him it's just a question of his personality allowing him this big move from Villarreal to Man United to Wembley.
"It was just that. He was super comfortable so no doubt that he's a man for us."