Similarly to last October's Premier League win over United, Chelsea fans often jeered and baited their old boss.
Mourinho responded by holding up three fingers to represent the Premier League titles he won across his two spells at Stamford Bridge and after the match he declared he was still their number one, despite supporters thinking he was "Judas".
And Wilkins, formerly a Chelsea player and assistant manager as well as a United player, felt Mourinho was unfairly treated by the home fans.
"I just wish our Chelsea supporters, and I'm a Chelsea supporter, showed a little bit more class to Jose Mourinho," Wilkins said to Sky Sports.
"He is a good bloke but he is a football man, he wants his club to win. I just thought the other night against Manchester United they didn't show him the respect he merits.
"People will naturally be thinking: 'Hang on a second he was demonstrating stuff on the touchline against Chelsea'. Well, yes he was, but now he is employed by Manchester United.
"Chelsea relieved him of his post. If we actually remember what he has done for our club, and I say our club because I have been a Chelsea man since I was 10 and a half, he has worked miracles there.
"I think they [Chelsea fans] do [think he is still number one] if they are thinking about it logically and sensibly.
"There is no one that that can touch him at the moment. Jose will be number one until somebody wins as many trophies as Jose."
Wilkins did not think the latest clash between Mourinho and Chelsea boss Antonio Conte on the touchline was a significant incident, after they also had a disagreement in last year's league meeting.
He added: "When you have got two coaches on the sideline that have so much passion then you are going to have a little [confrontation].
"You could have said Conte was disrespectful to Jose. It was just a conflict of interests, they just had a row and these things happen."