READ: Ronaldo opens Juventus account after 8 minutes
The defending Serie A champions have added global superstar Cristiano Ronaldo to their ranks in the off-season, as well as signing Emre Can, Joao Cancelo, Leonardo Spinazzola, and Leonardo Bonucci.
Allegri believes with the talent and experience he has in Turin, they should be challenging for that elusive UEFA Champions League trophy.
"Naturally, we have bigger ambitions of winning the Champions League than in previous years, just as we want the Scudetto, Coppa Italia and Supercoppa Italiana," he told Sky Sport Italia.
"Ronaldo has above all brought experience at international level and is an extra motivation for the younger guys to aim higher. You don't win five Ballon d'Or trophies for nothing and you can see how hard he works to get there.
"However, Real Madrid have won four of the last five editions of the Champions League and they did that through hard work. We've got to work, too, and this is the first time I've really seen the whole squad play together."
"This is a team built every year to achieve every objective," he added to RMC Sport. "We have more experience now, and there have been the arrivals of Ronaldo, Emre Can, Cancelo, Spinazzola will be available, the return of Bonucci.
"I would say the team has improved but you can talk about that all day long. There's a field of green where you have to play, you have to run, you have to have great respect for your opponents.
"This year, more than ever, we want to beat everyone."