There left-back was struggling with cramps late in the game as the Belgians forced extra-time in the Europa League quarter-final second leg at Old Trafford.
Mourinho admitted he thought about substituting Shaw for Ashley Young when Zlatan Ibrahimovic was forced off with a knee injury, but was given assurances by his player that he wanted to battle on for his team.
"I always trust the players with special mentality," Mourinho said. "Always trust them.
"Luke Shaw did something new today, it means a lot for me.
"After 90 minutes, before I know that I have to change Zlatan, he had cramp, I had Ashley Young ready to come on, and he told me I'm going to play for 30 minutes with cramps, no problem.
"He said if you need to make a change in another position I am ready for it.
"These kind of things make me trust the players."