The Citizens broke multiple records in the Premier League last season en route to the title, including an unprecedented triple-figure points tally.
However, Europe's top prize continues to elude them, with Liverpool emerging triumphant in their semi-final last term.
"Yes - I think, step by step, we're getting closer," Mahrez told ESPN when asked whether the Champions League was their primary target.
"It's still hard [to accept] that we couldn't achieve more than we did last season. Like always, this will be our target - to be better in this competition.
"It's really hard because you see the other teams and everyone is trying to get better to win the season and stop us too and the way we play, our tactics. We have to work hard to get more perfect in some situations."
Man City's only European title in their history remains the 1969-70 European Cup Winners' Cup.