Guardiola was left counting the cost of a fourth-round victory secured by first-half goals from Kevin De Bruyne and Raheem Sterling.
Sane failed to come out for the second half after Joe Bennett’s high tackle left the Germany winger with an ankle injury, and the Cardiff defender was sent off in the final seconds for another poor challenge on City substitute Brahim Diaz.
“He (Sane) will be out for a while - minimum two weeks, three weeks, one month, we will see tomorrow exactly,” said City manager Guardiola. “I said many times the only thing they (referees) have to do is protect the players.
“I can accept our disallowed goal, I don’t know why but I accept. But please protect the players. It happened once with Leroy, then it happened with Brahim again at the end.
“So for the football in general, and for the players who are the artists, they must do that. That’s why we are all here.”
City remain in the hunt for an unprecedented quadruple after booking their place in the last 16 of the FA Cup.
Guardiola’s side have a 12-point lead at the top of the Premier League, play Arsenal in the final of the Carabao Cup, and resume their Champions League campaign next month.
“There are no words to describe the pride I feel about my players and my team,” Guardiola said. “We have played many games and we do not have a big squad because of so many injuries and players with problems.
“Playing in the FA Cup away to a Championship team like Cardiff, who are at the top of the league, is so complicated, but we react again like a mature team. We are in the draw and hopefully we can have a team at home.”
Asked about some of Cardiff’s dubious tackling, manager Neil Warnock replied that Manchester City were not blameless.
“They dished it out a bit, they had one or two naughty tackles,” Warnock said. “He (Guardiola) is in England, what do you expect?
“I suppose when you’re like that, you want everything to be nice, pretty and perfect. But you don’t get that here, you get different challenges.
“They’re so quick, that’s the problem, with the movement and everything else, you think you’re there and all of a sudden he’s gone.”
But Warnock was critical of Bennett’s late red card, which rules the full-back out of next weekend’s crunch Championship trip to Leeds.
“I was disappointed he got sent off at the end,” Warnock said. “Obviously he doesn’t want to go to Leeds, because it was an absolutely pathetic challenge when he is on a booking.
“To do something like that I think is disrespectful to his team-mates.”
Etheridge, Richards, Morrison, Ecuele Manga, Bennett, Grujic, Ralls (Damour 88), Mendez-Laing (Feeney 78), Paterson, Hoilett, Zohore (Pilkington 67).
Tomlin, Halford, Murphy, Bogle.
Bravo, Walker, Kompany, Otamendi, Danilo, De Bruyne, Fernandinho, Gundogan, Bernardo Silva (Diaz 89), Sterling, Sane (Aguero 46).
Stones, Mangala, Adarabioyo, Ederson, Zinchenko.