The Bayern head coach guided the German giants to the Bundesliga and DFB-Pokal double last season, but he believes the squad cannot afford to become satisfied with what they have already achieved.
Speaking during Bayern's Audi Summer Tour in Hong Kong, where the club have been welcomed by thousands of supporters, Kompany said his focus remains firmly on preparing his side for another demanding season.
"It's not just about improvement, but I think we still need to have the same ambition we showed on day one. That hasn't changed," Kompany said.
The Belgian coach stressed that every player in the squad, regardless of their status, must continue striving to improve.
"We have to want to improve, that applies to our top players as well as everyone else on the team. And we have to want to win more titles and more games."
Kompany believes the key to maintaining Bayern's high standards is not simply the quality within the squad, but the attitude the players bring every day.
"It's more about mentality than quality, and that mentality must remain the same," he said.
Bayern are continuing their preparations for the new season in Asia and will face Premier League side Aston Villa in a friendly on Saturday before returning to Germany.
The Bundesliga champions will then host RB Leipzig at the Allianz Arena in their final pre-season match before beginning their bid to defend their domestic titles.
