The Gunners were saved by a quickfire double salvo from Andrey Arshavin and Park Ju-young as they continued their unbeaten League Cup run at the Emirates Stadium.
"The first half I believe we had the chances [to score] but in the second half we were caught straight away in losing the ball in our own half," said the Frenchman, whose side face Chelsea this weekend.
"They scored and from then on we were tested as the more experienced players took charge of the game, like Park, Arshavin and [Yossi] Benayoun. They made the difference.
"I have to congratulate the team as we had two young full-backs who are usually central players that played out of position.
"In midfield we were very young and we showed good spirit against a good Bolton side.
"When we were 2-1 up in the last 20 minutes, our legs had gone a little bit and we had to hang on, relying on a bit of luck because any players had not played at that level at that intensity.
"What was vital for us was not to go into extra-time."