McTominay, who had replaced Paul Pogba for United's goalless draw with Sevilla on Wednesday night, started alongside the Frenchman on Sunday as the Red Devils came from behind to beat the Blues at Old Trafford.
Mourinho has backed McTominay to have a growing influence in the United team in the future, adding that the midfielder could bring goals to his team.
"He is a fantastic player, a player that is a modern midfield player, he can do everything," the Portuguese manager told reporters after the game. "The only thing he's not doing yet is scoring goals, which he can, the only reason he isn't is because of the job I am giving him.
"I think in the future he can, we saw that in pre-season, bu I am very happy with him today. I don't like to individualise, Nemanja Matic also played very well in midfield, and the defenders too, and Alexis Sanchez made a huge effort too.
"In the second half we were more confident, I think if anyone deserved the win, it was us."
United are now unbeaten in three matches following their 1-0 defeat to Newcastle United earlier this month.