The Ligue 1 leaders progressed to the quarter-finals on the away-goals rule after Tiemoue Bakayoko's header 13 minutes from time sealed a 3-1 victory on the night at the Stade Louis II.
Leroy Sane's goal six minutes earlier had City on the brink of going through, with Pep Guardiola's side having shown ample improvement from a chastening first half where Kylian Mbappe and Fabinho were on target for the rampant hosts.
"We were very sloppy, not up to our standard in the first half. We wanted to correct that but we weren't clinical enough in both boxes," England centre-back Stones told BT Sport.
"We didn't create enough chances and we weren't defensively solid enough in the first half.
"The second half didn't reflect the scoreline. We were the City people know from this season. We should have scored more goals."
Stones scored his maiden Champions League goal during last month's rollercoaster first leg, where City twice came back from behind, but there would be no reprieve this time around.
"It's a difficult one for us to take," he said. "After the first game it was about how we came back.
"Now we're thoroughly disappointed. We know we should have done better and deserve to be in the next round."
The sight of Bakayoko punishing City's slack set-piece defending in the tie's decisive moment was particularly galling for Stones, who revealed his team-mates failed to heed a warning from Guardiola.
"The gaffer was saying before the game that the more and more he plays in the Champions League, the more it is about set pieces," Stones said.
"You saw Real Madrid the other week scoring from two set pieces and going through. We weren't solid enough in those areas of the game and that's what let us down."