Goals from Kevin De Bruyne and Raheem Sterling saw City safely past Cardiff City in Sunday's fourth round match in the Welsh capital.
That victory was soured, however, by Sane's withdrawal before half time following a nasty studs-up challenge perpetrated by Joe Bennett.
Bennett only received a booking for the hit before later seeing red for a separate offence, and Pep - who was spotted having a heated exchange with officials at full-time - believes Lee Mason was far too lenient in his refereeing.
"I don’t understand the (Bernardo) goal that we didn’t get, but that is okay. We can accept that. But they have to protect the players," Pep told reporters after the final whistle.
"They [refs] are there to protect the players. When there is fault, there is fault, and when it is dangerous, it is dangerous.
"We will see [Sane's injury] tomorrow, he could be out for two, three, four weeks."
It was not just Guardiola who was concerned by Cardiff's harsh tackling either, with the German national team having taken to Twitter at half time to ask the Welsh side to be more careful with their tackling ahead of Die Mannschaft's participation in the World Cup.