The Chelsea boss responded to suggestions he was playing down his side's title chances through a fear of missing out on top spot in the Premier League at the end of the season by labelling Wenger a "specialist in failure."
|11/4||Arsenal are 11/4 with William Hill to win the FA Cup|
"I do not want to go into silly, disrespectful remarks," he told BT Sport. "I did not speak about him in my press conference and I won't do so again tonight.
"All I know is that it is more embarrassing for Chelsea than for me."
However, Wenger went into further depth in the post-game press conference, adding: "I’m embarrassed for him, honestly.
"I think we’re here to talk about a football club. First of all I’d say I didn’t speak about him in my press conference. I have no more to say.
"I’m not interested in the subject at all - that is really, genuinely. If you’re interested and have nothing more to do with your life, that’s up to you.
"I love football. I’m sorry to disappoint you but I focus on what’s on the pitch."
Wenger saw Arsenal edge past Liverpool in the FA Cup and book a quarter-final meeting with Everton on Sunday, and was delighted with the character his side showed to respond to a 5-1 defeat at Anfield last weekend.
"Our mental strength, our mental response, our intensity from the start on - [I am] very proud of the way we responded after a huge defeat last week that was the most pleasing."