The Dane is linked with a move to Inter Milan and the Special One thinks the club's fans need to remember what he has achieved for them before giving him stick.
Asked about the playmaker's conduct amid continuing speculation linking him with a move to Inter, Mourinho said: "Christian played very well.
"Very professional. What I expect from him.
"If his decision is to leave, he has to leave with his head up. Fans have always to respect."
On the win over Middlesbrough, Mourinho added: "3-0 was so close so many times. I told my players at half time if we don't score 3-0 then if 2-1 we would be in trouble and it happened.
"We knew the opponents were hard. They brought on Gestede and went direct and made problems and when it was 2-1 we knew it was going to be difficult.
"We tried our best, the boys are trying their best. They dealt well with many set piece situations.
"We did lots of things well, we conceded the goal, a bit frustrating, but more frustrating was that we did not score three, four or five."