City dominated the Gunners for long periods and went ahead through Sergio Aguero, before Nacho Monreal equalised with 20 minutes remaining.
Yaya Toure and Fernandinho both hit the woodwork in the closing stages of normal time, before Alexis Sanchez fired a close-range winner in extra time.
City had a shout for a penalty in the first half and had a goal controversially disallowed – but Guardiola says there is no time to dwell on what could have been, with his side now focusing on achieving a win against fifth-placed United, who sit just one point behind City in the race for a top-four finish.
“We have three or four days to recover [before the game with United],” he said. “Today we are sad but as soon as possible we will stand up.
“We tried to change many things. Some days we did it but results show who you are, they could be better, could be worse.
“In games like this, a semi-final is like a final, you cannot expect control every situation but we control most of the time.
“They play long balls to [Olivier] Giroud and they counter-attack and with set pieces they are a tall team. They beat us because of this.”
According to SAP, City dominated possession (65 per cent) and created more chances (15 to Arsenal’s seven), yet were undone by a set-piece that led to Arsenal’s winner.
Guardiola says he was pleased with the overall performance of his team – and City’s FA Cup campaign as a whole - and vowed to make big improvements ahead of next season.
“We make a good performance; we play like you have to play a final,” he said. “We did absolutely everything to play, like yesterday Tottenham.
“Congratulations to Arsenal and Chelsea to achieve the final.
“We will improve next season and be stronger.
“We make a good cup performance. All the games away against Premier League teams. We arrive here and we compete, create more chances than our opponent, and hit the post.
“It was a little bit similar like what happened in the season.
“The teams does not need to do a lot of things score goals [against us]. We have some problem to score but we play like we want.
“At the end we are sad. Tomorrow we have to stand up and prepare for the games we have still to play.”