The Norway forward propelled City into the quarter-finals after a 7-0 win at the Etihad on Tuesday and underlined their determination to finally win Europe's elite club competition.
"Of course the club want to win the Champions League, they want to still win trophies," said Haaland, who has now scored a staggering 39 goals in 36 appearances for City since arriving from Borussia Dortmund last year.
"They've won the Premier League four times out of the last five years so they didn't bring me in to win the Premier League, they know how to win the Premier League," he told CBS.
"So, you can read between the lines. I'm here to try to help the club develop even more, to win the Champions League for the first time."
Haaland became only the third player to score five goals in a single Champions League game at the Etihad, taking his tally in the competition to 33 goals in 25 games.
He is the quickest player to reach the 30-goal milestone in the competition and, at the age of 22, the youngest.
Haaland also eclipsed Tommy Johnson's 1928/29 club record of 38 goals in a single season for City.
But he insisted his appetite for goals was far from satisfied and he hopes to get even better.
"I knew I was going to score goals because, last season, how many goals did City score? Probably a hundred.
"When I saw them last season without a striker I was thinking when they were crossing the ball in, I was like 'Ah, I'd love to be there'.
"In the end there is so much potential in this team and I think we can improve a lot.... It's an easy thing to say but I could have scored more goals. I missed a lot of chances."
City's performance emphatically dispelled any concerns after their 1-1 draw in the first leg last month.
Ilkay Gundogan and Kevin De Bruyne also got on the scoresheet as Pep Guardiola's men wrapped up an 8-1 aggregate success.
"The feeling is amazing," said Haaland, who has now scored five hat-tricks this season. "First of all to win 7-0 and to give a kind of statement in this tournament, the Champions League, which is a tournament I love."
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