Speaking after his Arsenal side moved into the quarter-finals of the FA Cup with a 2-1 win over Liverpool on Sunday, Wenger branded Mourinho's controversial statement as disrespectful.
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Mourinho made the remarks in the build-up to Chelsea's fifth-round clash at Manchester City on Saturday – which the London club lost 2-0 – and Wenger believes the Portuguese was out of order.
"I do not want to go into those silly, disrespectful remarks," he told BT Sport.
"I never spoke about him in my press conferences and I won't start now.
"It's more embarrassing for him than me."
Arsenal made it to their first FA Cup quarter-final in three years and will now face Everton in the last eight.
It came a week after their 5-1 defeat away at Liverpool in the Premier League and the Frenchman was pleased with his side's resolve.
Alex Oxlade-Chamberlain and Lukas Podolski put Arsenal 2-0 in front before Steven Gerrard pulled one back from the penalty spot.
The fifth-round tie ended in controversy when referee Howard Webb failed to award what looked a certain spot-kick when Oxlade-Chamberlain tangled with Luis Suarez.
"I'm very proud of the way we responded to the huge defeat last week," he continued.
"To win makes you stronger and that was very important. There were suspicions that we would sacrifice that game.
"I've seen the (penalty) incident, but I will have to look at it again. Maybe, maybe not."