The Premier League leaders underlined their desire to go one better than last season and finally win Europe's elite competition with a 5-0 victory over Sporting Lisbon in the last-16 first leg on Tuesday night.
Defeat in the final to Chelsea last summer halted City's chances of finally lifting the Champions League trophy, with the bookmakers making Guardiola's men favourites once again this term.
However, the Spaniard admitted there are a host of top teams who could stop them from being victorious in May, including Klopp's Liverpool side who won the competition in 2019.
"Last season in the Champions League, we played 14 or 15 games, won 12, drew one and we lost the final,' he told CBS Sport.
"So better performances in the Champions League than last season is impossible.
"People say 'this year we have to win the Champions League', we tried last season, two seasons ago as well. Every time we play we try to do it.
"The important thing is after six seasons together, especially the last five still, right now, after players won everything, still they fight for each other, look at Raheem [Sterling], look at Bernardo [Silva]."
When asked which team could beat them in Europe, Guardiola said: "Liverpool. They are six points behind us, Liverpool are the bigger rivals in the past seasons, always there.
"They are a pain in the ass all the time," he quipped. "They are a fantastic team in Europe. Just take a look at PSG today, they played really well against Madrid, look at Inter Milan or Liverpool or [Manchester] United.
"When you are the favourite, they don't assure you in April or May. In a long competition like the Premier League, when you win it you are the best.
"In the Champions League our goal [focus] is the next minutes, the next game because it changes everything. In the Premier League no [it doesn't] but in this competition it is like this."
Guardiola is unlikely to have his fears eased when he learns Trent Alexander-Arnold is targeting three trophies with Liverpool this season, despite the widening chasm at the top of the Premier League.
The Reds face Inter Milan on Wednesday night to continue their Champions League campaign and the England defender admitted he was not jealous of City's recent success.
"We don't feel disappointed we haven't won enough trophies because we feel the trophies we have won are the biggest and the best you can get your hands on," he said in his pre-match press conference.
"Obviously not making any digs but you look at Man City's amazing team and they haven't been able to lift the Champions League.
"They have won a couple of Prems but they have not been able to win the Champions League and we have won both in the last few years.
"There is an expectation now as a team, as players, to win trophies. I think one trophy a season is the minimum we need to be achieving.
"Next week [in the Carabao Cup final] we have the opportunity to go grab that but with the squad we have got, the manager, we should be winning trophies, we expect that of ourselves and if we don't it is a massive disappointment.
"We are not in that phase now where we are happy just to get to finals and it is a little bit of a surprise and a day out."