Shaw's future has been cast into doubt following public criticism from the Portuguese, after he questioned the commitment of the 21-year-old, who was signed by previous boss Louis van Gaal from Southampton in 2014.
Full-back Shaw missed most of last season through injury, and has struggled to hold down a regular place since Mourinho took charge nine months ago.
However, after insisting he will do everything in his power to be a success at Old Trafford, the full-back made a rare start in front of England manager Gareth Southgate in a 3-0 win at Sunderland that maintained United's hopes of qualifying for the Champions League by securing a top four finish.
Mourinho revealed how he considered substituting Shaw at half-time as a precautionary measure after he received an early booking, but decided against such a course of action for fear of it being misinterpreted as a latest snub towards the player.
"Luke was one of a number of positive performances ," he said. "He played well. The opposition was not creating big problems but he was solid and confident on the ball. He read the game well so it was good for him.
"I thought about a half-time change, but that was too harsh for him. I wanted him to play a little bit more, so then we're 2-0 up after an hour with their crowd asking for everything and putting the referee under pressure, I didn't want to take any risks because we have no players, and we need him to be available for the next match."
Goals from Zlatan Ibrahimovic, Henrikh Mkhitaryan and Marcus Rashford, who scored in the Premier League for the first time since September, stretched United's unbeaten league run to 21 games as they climbed to fifth, four points behind rivals Manchester City in fourth, with a game in hand.
Equally importantly for Mourinho, his depleted squad sustained no fresh injuries as they step up their preparations for the midweek Europa League quarter-final first-leg trip to Anderlecht in a competition which offers a Champions League place to the eventual winners.
Ecuador midfielder Antonio Valencia is the only one of the current casualty list likely to come into contention for the trip to Belgium.
Sunderland are likely to appeal the red card shown to midfielder Seb Larsson, but manager David Moyes was keen not to use the loss of the Sweden international before half-time as an excuse for a fifth defeat in six games which pushed his side closer to relegation to the Championship.
The beleaguered Scot ended a turbulent week on familiar ground, reflecting on a latest loss as the curtain prepares to fall on the club's 10-year tenure in the top flight.
Larsson earned a straight sending off for a challenge on Ander Herrera shortly before the interval, although replays showed the 31-year-old had won the ball before making contact with his opponent.
"We'll have a look at it," Moyes said. "I don't want to make out it's the referee's fault but he (Larsson) gets the ball, he touches the ball, and there's no contact at all. It's not even a booking."
Moyes has until Monday to respond after the Football Association asked the 53-year-old for his observations following the outcry in the wake of his threat to slap a female reporter following last month's draw with Burnley.
The former Manchester United manager faces a possible disrepute charge which carries with it a potential touchline ban and fine.
After Sunderland recorded a seventh match without a goal to leave them bottom and 10 points adrift of safety, Moyes added: "We won't talk about relegation until it's mathematically impossible to stay up even though there's no hiding that we're in a tough position."