Mourinho claimed Manchester United’s top-four hopes were now “impossible” after crashing to the Gunners.
Goals from Granit Xhaka and Danny Welbeck finally gave Wenger his first win in 13 attempts against Mourinho in the Premier League.
There is no love lost between the pair and Mourinho sarcastically praised the fact Wenger had finally emerged victorious against him.
Mourinho said: “Arsenal fans are happy and I’m happy for them. It’s the first time I leave and they’re happy.
“I leave Highbury they were crying. I leave the Emirates and they were crying, walking the streets with heads low. Today they leave with their scarves, singing.
“It’s a big club. You think I enjoy a big club like Arsenal not winning trophies? I don’t enjoy it. But today I tried to win.
“Arsene Wenger is not a small manager, he’s a big manager, to have that record of winning so many matches is not normal. Normal is win, lose, draw.
“I really don’t care about it today. No problems. We shook hands and during the game.”
But Mourinho insists their only hope of reaching the Champions League is to win the Europa League, starting with Thursday’s semi-final second leg against Celta Vigo.
Asked about his side’s chances of finishing in the top four, he said: “Impossible. For two reasons. Because we are not the ones playing one match a week in a great situation.
“And because we go with everything on Thursday and we don’t go with everything against Tottenham on Sunday. This is too much for us.
“It’s all on the Europa League. Everything for Thursday now. We made eight changes. We made eight.
“Of course, we knew we were not coming in our maximum power. That’s a decision. We want to try to win the Europa League – it’s more important than finishing fourth.”
Arsenal are still six points behind fourth-placed City with a game in hand, but Wenger is refusing to give up on their top four hopes.
He said: “We have still a chance mathematically and we need to some help as well from the teams around us.”