City ultimately cruised to victory at the national stadium, with Vincent Kompany and David Silva scoring after the interval, but the first half was a different story.
Pierre-Emerick Aubameyang wasted a good chance to open the scoring, and Aguero edged City ahead when he latched onto a long Claudio Bravo punt and lobbed David Ospina.
Mustafi caught flak for his role in the goal, the German defender appealing for a foul to referee Craig Pawson rather than chase the striker, and former England defender Gary Neville lambasted "spineless" play from the Arsenal man.
"He thought [so] yes," Wenger said if Mustafi had reported a push.
"I don't know, I haven't seen it again. From the outside, the push was not obvious. I don't know, was he pushed or not but he thought [so]. He expected the free-kick, yes.
"It's difficult for me to go into individual criticism after the game like that.
"You want to go home and analyse the game and individual criticism doesn't matter too much, we have to focus on our next game."
3 - No manager has lost more League Cup finals than Arsene Wenger (2007, 2011 and 2018), level with Alex Ferguson (who also won the trophy four times). Hoodoo. pic.twitter.com/eg92R1Ifba— OptaJoe (@OptaJoe) February 25, 2018
That next game sees Arsenal welcome City to the Emirates Stadium on Thursday, but Wenger does not expect familiarity to give him any favours.
"It doesn't help because they will be on a high and we have to recover from disappointment," he said. "So, they have the advantage."