Stefano Pioli wants to see Milan enjoy a deep run in the Champions League after the Rossoneri sealed their progress from Group E in emphatic fashion.
A defeat to Salzburg on Wednesday would have seen Milan crash out, but there was never any danger of that at San Siro as Olivier Giroud scored a double and added assists for Rade Krunic and Junior Messias in a 4-0 triumph that sealed second place in the group, behind Chelsea.
Pioli, who signed a contract extension earlier this week, was delighted with his team's performance as they qualified for the knockout stages for the first time since 2013-14, though he wants his players to kick on and reach the later rounds of the competition.
"This is only the first step," Pioli told reporters. "We must not stop mentally.
"We must not be happy to have reached the second round, but aim to go further. This group is hungry and wants to do everything possible and even more.
"We are the Italian champions, we are not here by chance. I have strong players, whoever draws us will face a strong team."
At 36, Giroud became the oldest player to score a Champions League double for Milan since Filippo Inzaghi did so against Real Madrid in 2010, with the former Arsenal and Chelsea striker also setting up Milan's other two goals.
Since Opta have collected such data for the Champions League (from 2003-04), Giroud is the third-oldest player to both score and assist a goal in a match, after Didier Drogba for Chelsea v Schalke in 2014 and Edin Dzeko for Inter v Viktoria Plzen this season, and Pioli was enthused by the France international's performance.
"He is a strong person, a great leader and a great worker," Pioli told Sky Sports.
"He does what a player of his level has to do. He is a point of reference. He is always smiling and motivated. He is helping us a lot to grow up."