Arsenal beat Monaco 2-0 in Monte Carlo last night but were knocked out of Europe 3-3 on aggregate due to away goals.
While it was familiar heartbreak for the Gunners, Monaco were celebrating their first Champions League quarter-final since 2003-04.
But Jardim was unhappy with Wenger, accusing him of being "disrespectful" to his side in the first leg at the Emirates, where they won 3-1.
"In the first leg, when I wanted to shake his hand, he did not thank me, so this time even though Arsenal did everything possible to go through, I chose not to thank him," the Portuguese coach said.
"I think so (that was disrespectful) and right now we are celebrating and think that Arsenal may be did not show all the respect that they should have during the first leg.
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Arsene Wenger and Leonardo Jardim shake hands - before the game
"Nobody was expecting us to be here. It's a great reward, so we have to give credit to the players for what they did."
Wenger was philosophical in defeat, admitting his team had left themselves with too much to do from the first leg.
"I don't believe we had a disappointing performance, it was a positive performance and you can take that into the end of the season," he said.
"It was a very difficult task. If you look at the numbers, we had a 98 per cent chance to be out, but we did fight and produced the game we wanted.
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Jardim was unhappy with Wenger after the game
"At half-time, the game could have been over with the chances we created, overall we pay (for the fact) that in the first game we did not produce the performance we wanted.
"Monaco played at home, had zero shots on target, and yet go to the quarter-finals.
"Football is not a fairytale, it is a matter of being realistic and being clinical, maybe a bit lucky as well, maybe that is part of the game.
"If you take a look at the shots on target in the two games, they were well rewarded, and were very clinical.
"They really surprised us in the first leg when we were too sure of ourselves on the night."
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