Pep Guardiola could lead Manchester City to an unprecedented treble on Saturday but has admitted his team must win the Champions League to be considered among the greats.

Victory over Watford in the FA Cup final would supplement back-to-back League Cup and Premier League titles but it irks Guardiola that City have not gone beyond the Champions League quarter-finals in three seasons under his management.

“We have had a fantastic couple of seasons but to be considered the best I think you have to win the Champions League,” he said. “Our standard in that competition has not been as good as the rest of our work, I admit. That is something we need to address because it is still our dream to win it.”

An away-goals defeat by Tottenham ended City’s hopes in Europe this season and their chance of winning all four major competitions. Guardiola believes a clean sweep might have been impossible had Spurs been beaten because the strain would have told on City in the Premier League.

“We only won the league by a tiny margin, we were pushed very hard by Liverpool, and if we had beaten Tottenham I am not sure we could have coped with the pressure and the extra fixtures,” he said. “I don’t think we would have been able to keep our focus because the Champions League is really tough, you are playing with emotions more than you are in other competitions and it’s so tight. One goal, one decision, one miss could cost you.”

People are praising City as the Premier League’s best ever side but Guardiola takes a more historical perspective. “Liverpool and Manchester United are the biggest two clubs in the Premier League – history tells you that,” he said. “You cannot fight against history, but we are making steps. We did a great job this season because Liverpool were incredible. We already know who our rivals will be next season and the level we will have to reach.”

Guardiola offered an apology to anyone offended by the chant sung on the plane carrying City players and staff back from their title win at Brighton. The song mentions Liverpool fans being “battered on the streets” and being “victims of it all”. City denied it referred to Hillsborough or Sean Cox but it was widely condemned, including by Martin Cox, who accepted it was not about his brother.

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“It was not what people say,” Guardiola said. “Do you think for one second someone could imagine we would give offence about Hillsborough or the guy who was hurt against Roma? It’s incredible to think anyone could believe that.

“Those were tragedies for the Liverpool people. We were happy for ourselves, but if someone was offended for another issue I’m sorry, I apologise, it was never our attention. We celebrated because we win the Premier League against an incredible contender.”

The manager confirmed he would stay to defend that title after being linked with the soon-to-be vacant position at Juventus, where Massimiliano Allegri is to step down at the end of the season.

“I will not be going to Italy; how many times do I need to say it?” he asked. “I’m staying here for two more seasons, as long as City still want me. I’m satisfied working here and I’m not going anywhere.”

City are under close Uefa scrutiny and could be banned from the Champions League as a punishment for alleged financial irregularities, fiercely denied by the club. Guardiola said: “You are innocent until proved guilty and right now we are innocent. We’ll see in the future but I trust the club, I have spoken with the chairman and the CEO – I know what they did. If we did something wrong we’ll be banned, but at the moment we are innocent even if people are waiting for us to be guilty.”

Raheem Sterling, the football writers’ player of the year, has said he is more proud of winning the Premier League than picking up personal awards – lovely as those accolades are – and is particularly keen on winning the FA Cup for the first time. “It’s a beautiful trophy and one I’ve never touched,” the forward said.