A Man City poll has recently showed that supporters would prefer to win the Premier League than the Champions League.
After seeing the result Pep Guardiola, Man City coach said fans need to be encouraged to support the Champions League.
City open their ninth successive home campaign in the competition today when they host Croatia's Dinamo Zagreb.
"I know for fans the Premier League is most exciting. But this competition is nice too," said City boss Guardiola.
"We are going to try and seduce our fans and say 'we can do it'."
The club reached the semi-final once, under Manuel Pellegrini in 2016. During Guardiola's time, they have reached two quarter-finals, which ended in defeats by Liverpool and Tottenham.
"We have done polls and people prefer, by far, to win the Premier League rather than the Champions League," said Guardiola.
"I don't know why but that is the reality of our club and we have to accept it. I think it is because, in the past, they were not in this competition.
"We want to win it but if we don't, I am not going to kill myself," he said.
"I have a feeling we are closer but this competition is a high level and I wouldn't want to arrive once in the final and then disappear for five years. That would not be good."