Arsenal fans chanted "boring, boring Chelsea" after Sunday's 0-0 draw with Mourinho's men at the Emirates, a result that virtually sealed the Premier League title for Chelsea.
The Portuguese responded by saying "boring is not winning the title for 11 years", referring to Wenger's failure to finish top with his north London club since 2004.
Asked about Mourinho's comments ahead of third-placed Arsenal's clash with Hull City on Monday, Wenger told reporters: "The biggest thing for a manager is to respect other managers. Some people have to improve on that".
The Frenchman has never beaten the Chelsea boss in 13 attempts and the pair have often clashed.
Last year Mourinho labelled Wenger a "specialist in failure" while at Stamford Bridge this season the duo were involved in pushing and shoving in the technical area.
Arsenal have not lost in the league since a 2-1 defeat to north London rivals Tottenham Hotspur in February but despite their fine run of form they are 13 points behind champions-elect Chelsea.
Wenger said it could have been a different story but for injuries at the start of the season.
"We have made progress so I look at it in a positive way," he added. "What you want to show during the season is that you are getting better. We were faced with a big challenge especially with Chelsea out in front.
"We had injuries to key players after the World Cup. We needed to find balance in the team. Looking back we dropped big points ... and that was a big disappointment."
Chelsea can seal the title with a win against Crystal Palace at Stamford Bridge on Sunday and Wenger believes their ability to grind out results is what sets them apart.
"Once you are fighting for the championship you win some games because you smell you can do it, games that you don't necessarily win if you are fourth or fifth. That doesn't always represent the value of the team," Wenger said.
"Manchester City had ups and downs and started stronger than us and were in front for a long time. Manchester United had a slow start and became stronger."
(This version of the story recasts with Wenger quotes)
(Reporting by Martyn Herman and Michael Hann, editing by Tony Jimenez)
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