Goals of great quality from Gabriel Jesus and Kevin De Bruyne secured the points for City, but the win was marred by what looked to be a hamstring injury to Stones midway through the first half.
On the positive side, Vincent Kompany returned for the first time in nearly three months and produced a typically commanding performance at centre-back after he had survived an early booking.
Guardiola said: “It is unfortunate for us and for John and I think he might be out for six weeks with that type of injury.
“We have to suffer as he plays for 90 minutes, and 90 minutes and 90 minutes. We don’t have a lot of central defenders. But the spirit in the team and with all the players is good so we are going to find a solution.
“I am really impressed with Vincent. After more than two months (out) and just one game with the national team it is so complicated to come back.
“But we know what a competitor and how strong he is as a defender both with the ball and without the ball. He helped us a lot at the end of last season to win seven games in a row.
“Hopefully he can be fit and safe for the next period of games.”
Leicester 0-2 City: Player stats
Eliaquim Mangala came off the bench to replace Stones and helped City to another clean sheet - but De Bruyne and Jesus will likely grab the headlines again.
Jesus won’t score an easier goal than this one - his 10th of the season - but the brilliance of it was in the build-up. Sharp, short one-touch passing involving De Bruyne, Fabian Delph, Raheem Sterling and David Silva simply dismantled the Leicester defence.
Then came De Bruyne’s virtuoso strike - a left-footed rocket that left Kasper Schmeichel clutching the cold evening air.
Guardiola declared: “The first was good because we did it after a lot of passes, and after we attacked the space and the decisions were good.
“After that Kevin, it’s his talent... last season we didn’t score that type of goal, he hit the post many times. This year it’s going in.
“It’s always complicated after internationals but I’m not surprised by my players. Here in Leicester it’s always complicated with throw-ins, corners, their movement in behind and Mahrez. We controlled the game again, we didn’t suffer and it’s three more points.”
