"That’s why we are here -- to win trophies for this football club and make it successful," Arteta told reporters.
Asked if the win would raise expectations too high for the Premier League season starting next weekend, he said: "I don't know. I just wanted to grab that trophy as quickly as possible and then we can think about the next.
"Just the joy of seeing so many happy and proud people and the connection again doing it for our supporters in Wembley feels very different, and that’s great," he said.
"We know it's football -- you win a trophy today but tomorrow you have to be training."
Arsenal's Leandro Trossard levelled the score with a deflected goal in the 101st minute, after Cole Palmer had scored for City in the 77th, sending the match to a penalty shootout.
English Football League referees are this season adopting new regulations to avoid wasting time by adding on the exact time lost in goal celebrations, substitutions or injuries.
Arteta said he was in favour of the new rules.
"I think it's really good to do that because it was going too far I think and now teams are going to have to think twice," he said.
"Now we have to be prepared to play 100 minutes because it's going to happen every single week."
City manager Pep Guardiola said it had been a close match between the two teams.
"In the last 15-20 minutes of the first half they were better. Second half we were much better," he told reporters.
"We would love to win today, absolutely, but sometimes you have to accept it and give credit to your opponent."
Guardiola said his side had to get used to longer added time.
"We have to accept it. Now games will be 100 minutes that’s for sure," he said.
