City won 2-0 at Wembley with Nico O'Reilly scoring both goals. The result means Arsenal remain without a trophy since 2020.
Arteta said afterwards: "It's painful when you get to a final and you have that will to win the first trophy of a season after eight months working on it is always tough.
"We had the best chance of the game to put it 1-0 and the game would be different. They had two shots and scored two goals.
"They were two different halves. The first half was very positive in every sense, the second half was a different one. You have to give credit to the opposition.
"We had opportunities to break, we gave the ball away. When we regained the ball we gave it straight back."
On the importance of staying calm, Arteta added: "We had great incredible months together. Today is a disappointment, football is part of that.
"We have to use the fight to have two amazing months at the end of the season."