The two managers argued on the touchline during the game, with the Arsenal boss complaining to the fourth official that Hughes had left his technical area.
After the final whistle, Wenger walked straight down the tunnel with Hughes waving at him from the side of the pitch.
Wenger is now preparing his side for Saturday's home game with Stoke and insists that he has nothing to apologise for.
"I don't deny that I am a bad loser but on this occasion I would have done exactly the same if we had won or lost the game," he added.
"I act in accordance with the principles I think are important on the football pitch and I maintain exactly what I said and did."
When asked if he had been insulted by Hughes, Wenger responded: "I'm used to treating this kind of thing with the needed distance. I do not want to make a fuss.
"There are incidents on the touchline but you never heard me ever say anything about another manager after the game, in a press conference or after during the week.
I think it's a good thing to maintain calm and the atmosphere
Chelsea manager Carlo Ancelotti on the practice of shaking hands
"I maintain exactly the way I behave and do not regret one second of what I did."
For his part, Hughes is keen to move on from the controversy.
"We keep revisiting things that have already occurred," he said. "Everybody has had their say on what happened.
"I have my view, as I tried to articulate after the game. I am sure Arsene has his view on it as well. But that is between myself and Arsene, not anybody else.
"It is not something I am not looking to dwell on. It is past, why revisit it? We are grown men, we just get on with it. From my point of view the issue is over."
Cheeky journalist winds up Hughes
City host Premier League leaders Chelsea on Saturday and Blues boss Carlo Ancelotti insists he likes the practice of shaking hands after the game.
"I think that shaking hands is a normal thing," Ancelotti said. "Mark Hughes is a very good coach. I know him. For me, it's not a problem to shake hands. You show respect to the other coach. It's normal.
"In Italy, it's not usual to do that at the end, immediately after the game. In England we have to do it. I think it's a good thing to maintain calm and the atmosphere.
"I don't know why Wenger didn't shake hands with the other coach. I don't know if it was right or wrong. Every person can do what he wants to do."
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