Cardiff midfielder Bennett was only booked, though television replays showed that the challenge might have been worthy of a red card. Bennett was then sent off in added time after another crunching foul on teenager Brahim Diaz.
Guardiola was clearly angered by Cardiff's physical approach and animatedly spoke to referee Lee Mason after the game.
Speaking about Sane in his post-match news conference, Guardiola said: "He will be out for a while, minimum two to three weeks or a month. We will see tomorrow exactly."
Guardiola wants referees to do more to protect the players, who he labelled as artists, from being repeatedly fouled.
"I have said many times, all the referees have to do is protect the players - not just the Manchester City players, all players," added the Spaniard.
"It's not because one player is more brave to kick. The only thing the referees can do is to protect the players. It kept happening.
"So for the football in general and the players - because they are the artists - we need to care of them. I've said it many times but they need to protect them."
Cardiff manager Neil Warnock did not defend Bennett, who will now suspended for Saturday's Championship game against City's promotion rivals Leeds United.
"It is unprofessional from Joe and then to commit one in the 92nd minute," said Warnock. "Maybe he does not want to go to Leeds on Saturday. He will be training morning, noon and night, I can tell you that."
Bennett later wrote on his Twitter account: "Just want to apologise to Leroy Sane for my tackle today. I tried to stop the counter attack and completely mistimed my attempt.
"I didn't mean to catch him like I did. I hope it's nothing serious and he recovers quickly.
However, Warnock defended Cardiff's approach to the game and added that Guardiola should know what to expect, saying: "He's in England. They (City) did a few as well."
(Reporting by Neil Robinson; editing by Ken Ferris)
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