Guardiola, who signed a two-year contract extension last month, has guided City to four Premier League titles but failed to win Europe's elite club competition with them, a runners-up finish in 2020-21 their best result.
The Spaniard won the trophy twice with Barcelona, in the 2008-09 and 2010-11 seasons.
"It's not the only one but I admit it's the trophy we want and my period here will not be complete if we don't win it," Guardiola told reporters before Thursday's League Cup fourth-round clash against Liverpool.
"But that's not the only reason (I signed). I will do everything in the time we have together to win it but I'd say the same before (signing).
"It's the trophy we don't have and we'll try to do it. I have the feeling they (City) will get it sooner or later."
City, who are second in the Premier League and trail leaders Arsenal by five points, host Liverpool in the League Cup later on Thursday before travelling to Leeds United in the league on December 28.
