City led 5-3 after the first leg but trailed inside 10 minutes when Kylian Mbappe stabbed home from close range, with Fabinho levelling the scores on aggregate before the interval.
Leroy Sane struck from a tight angle after 71 minutes to nudge City back in front but a Tiemoue Bakayoko header from Thomas Lemar's set-piece completed the scoring and sent the hosts through on away goals.
Guardiola hailed the improvement of his side after the break but accepted City did not perform in the first half of the game, replying "45 minutes" when asked why City had failed to reach the quarter-finals.
It is the first time the Catalan has exited the Champions League at the last-16 stage in his coaching career.
5 – Man City are the first team in Champions League history to be eliminated in a knockout tie after scoring 5 goals in the first leg. Wild.— OptaJoe (@OptaJoe) March 15, 2017
"We played an exceptional second half but in the first one we forgot to be there," Guardiola told BT Sport. "We are a team who wants to defend aggressively without the ball. In the second half we were much, much better but it was not enough.
"This happens, the opponent was there and we will learn. We have a team with not a lot of experience in these competitions. In the second half we had the chance to score a lot of goals. We didn't and that is why we are out."
Guardiola was particularly disheartened to see a straightforward Lemar free-kick into the box converted by Bakayoko to score the pivotal goal in the tie but City's overall showing disappointed the 46-year-old.
"It is about the little details - set-pieces are so important at this level - but in the first half we weren't like we are," Guardiola said. "That is the only thing I am sad about.
"The opponent can beat you but we were not there and we should have been there. We are going to try to improve but the competition is so demanding and sometimes you have to be a bit lucky in these moments. We were not lucky."