City dominated possession throughout the game but were hit on the break twice by Pierre-Emerick Aubameyang.
The loss means the Champions League is City’s last chance of adding another trophy this season. They face Real Madrid in the second leg of their last-16 tie on August 7, holding a 2-1 lead.
"We know the standards we need at this stage of competitions," said Guardiola.
"Maybe we are learning, maybe now we will see. It doesn't take a genius to know we have to increase the standard for Madrid."
He added to BT Sport: "We wanted to play the [FA Cup] final to be in rhythm one week before the Madrid game. We missed this chance.
"We didn’t play good. The only regret is not losing the game, that can happen in football, it’s not playing the first half like we played the second. When you play like the second half you can lose. We didn’t play good; on the day when you have to we didn’t.
"We were not good…in these games you have to play good to go through."
Arsenal head coach Mikel Arteta hopes the result will go some way to convincing Aubameyang to extend his stay at the club, with his current deal set to expire next summer.
"Hopefully it will help him to be more convinced we are going in the right direction," he said.