The Citizens saw their 5-3 advantage evaporate in double-quick time at the Stade Louis II, as the free-scoring French side found the net twice inside the opening half-hour.
Leroy Sane's goal to again put City ahead in the tie was ultimately cancelled out by Tiemoue Bakayoko just six minutes later, with Guardiola failing to reach the semi-finals for the first time in his managerial career.
Speaking to BT Sport after the match, the former Barcelona and Bayern Munich boss said: "We played an exceptional second half but we forgot to do that in the first. We wanted to defend aggressively. We were better in the second but it wasn't enough.
"Normally we play to a good level but here we didn't. We will learn. The team does not have a lot of experience. The second half we had the chances and we didn't take them and that is why we are out. And set pieces are so important at this level.
"Barcelona and Real Madrid scored from them last week. We were not there and we were not there in the first 45 minutes. We will improve but this competition is so demanding. Sometimes we have to be special and be lucky. We were not."
Monaco join Bayern Munich, Borussia Dortmund, Atletico Madrid, Barcelona, Real Madrid, Leicester City and Juventus in the hat for the last eight.