Eriksen played the full 90 minutes as Spurs beat Sky Bet Championship side Middlesbrough 2-1 in their FA Cup third round replay in North London on Tuesday night.
The Dane has reportedly agreed a move to Serie A giants Inter and could leave this week after rejecting a new deal at his current club.
He has been accused by some sections of failing to put 100% commitment into his performances and was booed when the teams were announced before kick-off.
However, if he does leave, Mourinho wants him to be proud of his achievements at Spurs.
“He played very well,” The Spurs boss told the media.
“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.”
Mourinho didn’t provide an update on the Tottenham’s chase for Gedson Fernandes.
The 21-year-old is expected to join on an 18-month loan deal from Benfica with Spurs holding an option to buy.
“Any news? No news. I didn’t want to know anything during the day,” he continued.
“During the day it was just about the game. He (the club’s press officer) doesn’t have news for me so nothing.”