The Dane has reportedly agreed a move to Inter Milan and could leave this week after rejecting a new deal at Spurs.
He has been accused of downing tools this season and was booed before kick-off in Spurs' 2-1 victory against Middlesbrough in their FA Cup third-round replay on Tuesday night.
But if the former Ajax star does leave, Mourinho wants him to be proud of his achievements at Spurs, having been at the forefront of the team that has been among the best sides in England over the last few years.
"He played very well," he said. "Played very well, very professional which is what I expect from him.
"If his decision is to leave I think he has to leave with his head up, if he gives everything which is what he tries to do for the team. Fans, it's always to respect, we have to respect but I think the boy did it for us."
Meanwhile, Mourinho was unable to provide an update on the club's pursuit of Gedson Fernandes, who is expected to join on an 18-month loan deal from Benfica.
He added: "Any news? No news. I didn't want to know anything during the day. During the day it was just about the game. He (the club's press officer) doesn't have news for me so nothing."
Spurs, who are currently sat in eighth place in the Premier League table, are back in action on Saturday when they make the trip to Vicarage Road to take on Watford.
Tottenham cannot afford to slip up, as Mourinho's side now find themselves nine points off the top four.