Mourinho responded to 'boring, boring Chelsea' taunts from Arsenal fans by mocking the Gunners' wait for the title and Wenger was unimpressed.
Photograph: Stuart Macfarlane/Arsenal FC via Getty Images. Press Association
Arsene Wenger has hit back at Jose Mourinho and accused him of lacking respect.
Mourinho responded to 'boring, boring Chelsea' taunts from Arsenal fans last week by saying: “’Boring’ I think is 10 years without a title.
“That's very boring. You support the club and you're waiting, waiting, waiting for so many years without a Premier League title, so that's very boring.”
That was a clear reference from Blues boss Mourinho to Arsenal last winning the title in 2004.
Wenger responded by saying: "The biggest thing of managers is to respect each other and some people have to improve on that.
"You can have incidents with other managers. It is a bit heated when you fight directly with them but in the end time heals and what is the most important is to respect each other as much as you can."
Pressed further on Mourinho's conduct, Wenger added: "Everybody lives with his own internal problems and I live with mine and that is enough.
The Gunners boss also admitted he felt his side had made progress as they bid to finish above both Manchester clubs in the race for second.
"We have to look at it in a realistic way. I feel we have made progress and so I look at it in a positive way because what you want in the season is your team to become better," he added.
"We faced a big challenge because Chelsea didn't drop their level and that's why we didn't catch them but overall we have made progress."
Wenger revealed the contract situation surrounding Mikel Arteta and Tomas Rosicky will be sorted out at the end of May, before dismissing the apparent need for a new goalkeeper this summer.
"I believe in the goalkeepers we have," he said.
"Wojciech Szczesny is a good goalkeeper and David Ospina has come in and done a very good job. Look at the numbers and you will see Ospina is the top in the Premier League."
Mathieu Debuchy faces a race against time to be fit for Monday's trip to Hull but Alex Oxlade-Chamberlain is still out.