He made the desperate plea after watching his side thrash Crystal Palace 5-0 to stay top.
City supporters jeer the Champions League anthem when it is played before games believing the club has been persecuted in the past by UEFA.
But Guardiola said: “I hope the fans will come on Tuesday to help us.
“I know the fans have a problem in this competition but we need them.”
Manchester City were put in Group F with Shakhtar, Napoli and Feyenoord.
They enjoyed a perfect start in the first game as they beat Feyenoord 4-0 away.