The Red Devils went it at the break a goal to the good thanks to Daley Blind's effort but struggled to test Black Cats keeper Jordan Pickford.
United pulled clear in the second half thanks to goals from Zlatan Ibrahimovic and Henrikh Mkhitaryan before Fabio Borini grabbed a consolation at the death.
"I didn’t like the first half performance," Mourinho said. "I like the result. I liked very much the second half. The first half I didn’t like. I was expecting us to start much better.
"I know David Moyes and Sunderland deserved credit for what they did in the first half.
"Second half we had everything back intensity recover the ball high in the pitch play fast passes and to have players like Anthony Martial and Henrikh Mkhitaryan on the bench helps.
"We deserve the victory."
United have won their last four games on the spin but Mourinho believes his side can show more than they did against Sunderland.
"We have played well for a long time," he said. "I think our game against Burnley was absolutely phenomenal. We played better against Burnley than today.
"The good performances we had for quite some time. Finally we have the good results, four victories and 12 points in a row.
"The players know the principles of how we play and they are comfortable but we need to improve."
