Pep Guardiola wants to build on the work of his predecessors and help establish Manchester City among Europe's elite.
City open their Champions League campaign against Borussia Monchengladbach on Tuesday night on the back of four straight Premier League wins, the latest a derby success at Manchester United.
But having seen City's European progress halted by Barcelona and Real Madrid in each of the past three seasons, the manager has told his side to hit a new level if they are to better last year's run to the semi-finals under Manuel Pellegrini - their best result to date.
Speaking at his press conference on the eve of the Etihad game Guardiola said: "It was a pleasure to coach Barcelona and Bayern Munich for their history - they're used to reaching semi-finals but City don't have that history.
"Roberto Mancini helped us to take the first step and Manuel made a real good job to reach the semi-finals. He was unlucky to face Barcelona twice [in 2014 and 2015] as they are the strongest team in the world.
"Always you can play better or work better. That's the fascinating thing about this job. We are going to try [to win the Champions League] and we will see our level. If we do not achieve our dreams then we will think, what can we do better to do better?
"We are far away from the best we are looking for from this team - to compete with the best teams in Europe and in the Premier League. We have to improve."
The immediate task facing City is to overcome a Gladbach side Guardiola knows well from his time at Bayern.
"Borussia are a brave team, a brave coach - one of the best teams in Europe. If we let them play, they have a lot of quality. The draw was difficult for us - of course because of Barcelona but also Monchengladbach.
"They are so, so intelligent. The players in the middle - they are so, so offensive. They receive five players behind our midfield. They counter-attack like a master. Like a German team. They do it well.
"They have a good build-up - Yann Sommer is a goalkeeper who isn't tall but he reads the game. A little bit like we're looking for with short and long passes. They create a good environment for a good way to play. They are a really, really good team."
Guardiola again defended his own goalkeeper Claudio Bravo's performance at Old Trafford, describing the debutant as "so strong" - and said Ilkay Gundogan and captain Vincent Kompany are "almost there to help us play the next six games in the next 18 days."
City will also have Sergio Aguero available as his three-match ban for elbowing Winston Reid applies only to domestic football.