Despite losing at home for the first time since December 2016, City still progressed through to the quarter-finals 5-2 on aggregate following our 4-0 win away in Switzerland in the first leg.
But Stones, who came into a much-altered City side with manager Pep Guardiola making six changes from the team which beat Chelsea 1-0 last Sunday, said the players would respond in the right way to the result.
"We wanted to make sure that we got through to the next round and better ourselves from last season," said the England defender.
"Being knocked out by Monaco last season hurt so we wanted to put things right this season.
"But we're not happy with how we played tonight. We wanted to win and see it through that way.
"There's a lot of things we need to look at moving forward, both individually and as a team. We weren't at our best.
"We set high standards for ourselves and were disappointed that we didn't meet those standards.
"We have a good mentality and we know that we have got to take it game by game. The lads did the job out there winning 4-0 and it is one of those competitions where you have to take it game by game.
"But we are into the next round and now we need to go again."