Some Gunners fans chanted “boring, boring Chelsea” during last weekend’s goalless draw at the Emirates Stadium, which moved the Blues a step closer to the Premier League title for the first time since 2010.
In his post-match press conference, Chelsea manager Mourinho responded by turning the tables back on Arsenal, who last won the English top flight with the ‘Invincibles’ of 2003-2004.
There is certainly no love lost between Wenger and Mourinho, the pair having squared up in the technical area at Stamford Bridge earlier this season.
The Arsenal boss was given the opportunity to respond when he spoke to the media on Friday morning ahead of the Barclays Premier League match at Hull on Monday night.
When asked what he thought of Mourinho’s comments, Wenger replied: “The biggest thing for a manager is to respect other managers. Some people have to improve on that.”
Asked if Mourinho should conduct himself with more dignity, the Arsenal manager answered: “Look, everybody lives with his own internal problems and I live with mine. That’s enough.”
Chelsea held a press conference later on Friday ahead of the match with Crystal Palace on Sunday, when they could seal the championship.
Mourinho was given the chance to respond to Wenger’s earlier statements, but waved away any questions on the matter.
Wenger has endured his fair share of touchline bust-ups down the years, the fiery relationship with former Manchester United boss Sir Alex Ferguson the subject of many a back page.
The 65-year-old, though, believes coaches must eventually put a distance between professional and personal disagreements.
He added: “You can have incidents with other managers sometimes. It gets a bit heated when you fight directly with them, but in the end I believe time heals and the important thing is to respect each other as much as you can.”
Failure to beat Chelsea effectively ended any already slim hopes of a late title push, the Gunners now some 13 points off the pace after the Blues won at Leicester in midweek, although with a match still in hand.
Arsenal could be down to fourth place by the time they kick off at Hull on Monday night.
Wenger was asked if he felt the deficit was a fair reflection of the difference between the two sides, with Arsenal having enjoyed a superb run of form in 2015 following a poor start.
“That is always very difficult to say because when you fight for the championship, you win some games because you smell you can do it, not because you’re fourth or fifth. It doesn’t always represent the value of the team,” the Arsenal boss said.
“The gap is a gap and they have been more consistent than us from the start of the game. They had a very strong start and that kept them going until the end.”
Wenger has a near full-strength squad to choose from, with full-back Mathieu Debuchy doubtful because of a hamstring problem.
Midfielders Abou Diaby and Alex Oxlade-Chamberlain could also come back into contention before the end of the season, along with captain Mikel Arteta.
“He makes progress week by week, but needs more time,” said Wenger, who expects both Arteta and Tomas Rosicky to agree new deals.
Arsenal have been linked with a summer move for an experienced goalkeeper, including Chelsea veteran Petr Cech.
Wenger, though, indicated that was an area which he had confidence already.
“I believe in the goalkeepers I have,” added the Arsenal boss.
“I believe that (Wojciech) Szczesny is a very good goalkeeper and (David) Ospina has come in and done a fantastic job.
“You look at the numbers in the Premier League and who is top of all the goalkeepers and you will see it is Ospina.”