While Pierre-Emerick Aubameyang struck either side of half-time to book the Gunners’ spot in the final, City looked a much improved team after the break.
“We didn’t play good, the regret is that we didn’t play the first half like we did in the second,” Guardiola said after his side’s 2-0 loss at Wembley Stadium.
“When you play like we did in the second half, maybe you can lose, but we didn’t play good. On a day when you have to, we didn’t.”
In a season in which City have won the League Cup and are set for a second-place finish in the Premier League, they must now turn their attention to the Champions League.
Guardiola’s players take on Real Madrid in the second leg of their quarter-final on 7 August.
City won the first leg 2-1 at the Bernabeu and will return to the Etihad to finish the tie.
“Now we have two weeks,” Guardiola said.
“We wanted to play the [FA Cup] final one week before the Madrid game to be in rhythm, but we missed this chance.”