De Gea, 26, was a surprise omission from the United first-team with Sergio Romero starting ahead of him on Wearside with Joel Pereira his back up on the bench. Ahead of kick-off, Mourinho dismissed any suggestions his top shot stopper had been dropped, telling Sky Sports that a "little problem" meant he was unable to travel to the Stadium of Light.
Mourinho added the Spain international "should be back next week", with United welcoming Premier League leaders Chelsea to Old Trafford on Sunday 16 April.
Mourinho's comments suggest De Gea could be available for Thursday's Europa League quarter-final first leg clash against Anderlecht in Belgium. However, Romero has been United's preferred choice in European competition this season, having started seven of their 10 games in the Europa League this season.
Romero, who was brought to the club by Louis van Gaal in 2015, was untested for the most part during his side's comfortable win at Sunderland but produced one wonderful save to deny the hosts an equaliser in the first-half.
It was Victor Anichebe who almost found a way through, expertly turning Eric Bailly inside the six yard area before letting a shot away. His powerful effort was blocked by Romero, however, who enjoyed a far quieter second half.
Zlatan Ibrahimovic opened the scoring for United after half an hour with a splendid effort on the turn from just inside the Sunderland box. David Moyes' side were reduced to 10 men just before half-time when Seb Larsson was shown a straight red card for a challenge on Ander Herrera.
Just 48 seconds into the second-half, Henrikh Mkhitaryan doubled his side's lead with another precise finish before Marcus Rashford added a late third late on.