"I don't want to go into those silly, disrespectful remarks," said Wenger.
"The only thing I know is that it's more embarrassing for Chelsea than for me."
Wenger also denied speaking directly about Mourinho when he suggested rival managers were playing down their Premier League title chances because they were afraid of failure.
Those comments provoked a stinging response from Mourinho, who mocked Wenger's eight-year trophy drought at Arsenal.
"He is a specialist in failure, I'm not," Mourinho told a press conference.
"If supposedly he is right and I am afraid of failure it is because I don't fail many times.
"He is a specialist because eight years without silverware is very long. If I do that with Chelsea, I leave and I don't come back."
Wenger made his point on Sunday, as Arsenal bounced back from last weekend's 5-1 mauling at Anfield to beat Liverpool 2-1.
On Saturday, Chelsea crashed out of the FA Cup with a 2-0 defeat at Manchester City.
Earlier on Sunday, Arsenal legend Bob Wilson described Mourinho as "a boring bully".
He said: "I think at best it was disrespectful, at worst despicable to be so dismissive of a genuinely good guy and a footballing man I think, whose presence in England in 17-18 years has opened eyes and ears and created wonderfully entertaining sides.
"It's obviously not the first time Mourinho has singled Arsene out. He called him a voyeur which is a disgusting claim and thankfully on that occasion he - although belatedly - he did apologise.
"I think it's personal, he is a hugely talented, amazing manager Mourinho but I find - at this moment - I find him boring at the moment."