The former Borussia Dortmund striker missed a gilt-edged chance to give the Gunners the lead inside the opening 10 minutes, only managing to hit Claudio Bravo, as Kyle Walker put in a last-ditch challenge.
His profligacy was punished soon after when Sergio Aguero took advantage of limp defending from Shkodran Mustafi to put Pep Guardiola's side ahead, before Vincent Kompany and David Silva added gloss to the scoreline in the second half.
Wenger admitted that his side's defending was not good enough but was quick to highlight Aubameyang's miss as a crucial moment in the game.
"I felt we had the first good chance – a very easy one that we missed," he told Sky Sports.
"After that we made a big mistake for their first goal.
"We controlled them pretty well in the first half, but they came out in the second half, and we were unlucky because the second goal was offside. But congratulations to Man City, they deserve the win.
"When you lose a game, you have to cope with being criticised. Emotionally after a game – particularly a final – you do not want to go too much into criticism.
"We must recover quickly – we came to the final and we lost but we have to focus on the next Premier League game [against City on Thursday].
"When you lose 3-0 you have to look at defending better. When you lose concentration against quality teams you pay for it.
"It's not application that was missed – it was lapses of concentration and a bit unlucky as well."