City fans have booed the competition's pre-match anthem since 2012, following a €30,000 fine for their players coming out late for the second half against Sporting Lisbon.
The protests have intensified since 2014, when the club was fined £49million for breaching Uefa's Financial Fair Play (FFP) regulations.
And the revelation last week that Uefa are investigating City's compliance with FFP once again is likely to lead to further protests before Wednesday's last-16 tie against Schalke.
Guardiola, however, believes that City's fans are warming to the Champions League as a competition and feels their support will be crucial in reaching the last eight.
"I think the last time there were less boos," Guardiola said. "My feeling is now the people are starting to enjoy this competition. They are feeling like we can do it together."
City lead 3-2 from the first leg, played in Schalke's home of Gelsenkirchen three weeks ago, and they are hoping to reach the quarter-finals for the third time in four years.
"Alone we cannot do it, we cannot go through, we cannot make a good performance," Guardiola said.
"For example, Liverpool this season in the Premier League or last season in the Champions League, we were with them [the fans]. That is what we want."
Despite winning three Premier League titles since Sheikh Mansour's 2008 takeover and being on course for a fourth, a Champions League title remains elusive.
The club has never lifted the European Cup in its 124-year history, coming closest in 2016 when they finished as beaten semi-finalists under Manuel Pellegrini.
Guardiola described City as "teenagers" in the competition by comparison to other clubs with more illustrious European histories.
"We could win of course and make another step but you said numbers that you need to 20 or 30 years to try to win," he claimed.
"Of course we can arrive in the last stages and make another step forward, I cannot deny that. But I think to compare with those teams, one silverware doesn't change it.
"We are teenagers in this competition, that's what I feel. We want to win it, we push ourselves. The best way is to feel this kind of pressure."
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