Stefano Pioli insisted Milan had "nothing to be ashamed of" after an imperious Atalanta side condemned them to a second Serie A defeat of the season.
Having seen their unbeaten start to the campaign ended by Juventus on January 6, the Rossoneri suffered a second loss in four league games as they fell 3-0 to Atalanta at San Siro on Saturday.
Cristian Romero, Josip Ilicic and Duvan Zapata scored in a one-sided victory that stretched Milan's winless run against Gian Piero Gasperini's side to seven in the top flight.
However, Milan were confirmed as winter champions as Inter's 0-0 draw at Udinese means they will be top of the table even after each side in the league has played 19 games.
Pioli watched his team muster just two shots on target as a club-record run of scoring in 38 consecutive league games came to an end.
But the coach sees little reason to be overly concerned about losing to the reigning champions and an Atalanta side who have recorded 36 points from their first 19 matchdays, their best return in a 20-team division.
"We started well, with a lot of players in attack," he told Sky Sport Italia.
"They played very well. I'm disappointed with how we conceded the first goal from a dead ball, and the second one killed the game.
"It wasn't supposed to be like that, we could have done more, but we didn't manage it. Atalanta's strong points were evident, but we had to play better from a technical point of view.
"They were stronger than us tonight, but we're strong regardless. A game like this can happen. We know the league is competitive and difficult.
"I think defeats to Juventus and Atalanta are nothing to be ashamed of. Atalanta were physically superior, more intense, winning all the duels and the second balls as well.
"It's tight when you reach this level. We'll analyse the defeat, try to see where we can improve and focus on the next match."
Milan face Inter in the Coppa Italia quarter-finals on Tuesday before heading to Bologna next Saturday in Serie A.