Mourinho was seen shouting at Shaw during the first half of Saturday's quarter-final tie before substituting him at the break, later insisting that he wanted the Red Devils "to defend better".
"He is looking for a reaction from Luke," Wilkins, who starred in midfield for Man United during the 1970s and 1980s, told Sky Sports News.
"I feel for Luke a little bit because when he was at Southampton he looked an outstanding prospect at left back and it was a good move for him to move to Old Trafford.
"But I've said on numerous occasions - when you go to Old Trafford, it's not only what you can do with the ball, you've got to have the mentality of a winner as well and perhaps Jose is not quite seeing that in Luke at this moment in time."
Shaw has made just 15 appearances for Man United in all competitions this season.