The United boss argued his side should have been awarded a spot-kick when Maya Yoshida appeared to handle inside the penalty area, as Jesse Lingard attempted to break the deadlock at Old Trafford on Saturday.
As the England international juggled the ball 18 yards from goal, Yoshida's right arm connected with the ball, but referee Pawson deemed the incident not worthy of punishment.
"I think it is a disappointing afternoon for Craig because he's a fantastic referee, one of the most promising in Europe," the Portuguese told BT Sport. "It was one of the key points [of the game].
"We missed easy chances but I'm really unhappy with the penalty — not with Pawson's performance.
"I think Craig had a good performance, it was a big decision to make from him."
United's problems were added to as Romelu Lukaku was taken off on a stretcher following a nasty clash of heads after just eight minutes, while Mourinho confirmed afterwards that Zlatan Ibrahimovic will also miss the next month with his knee problem.