Manager Stefano Pioli is happy that they now have the chance to move on from that loss in a different competition.
"It hasn't been easy, we had a great deal of expectation surrounding the derby, there was a lot of positivity and confidence, and it went how it went, badly," Pioli told reporters on Monday.
"It was a huge disappointment but we have the Champions League now, thankfully, because it's the only way we can actually try and switch our focus."
Milan went out of last season's Champions League to their rivals Inter at the semi-final stage, and the league defeat on Saturday means they have now lost all five derby games in 2023.
"I'm in debt to the fans because last season when we played really badly they always got behind us," the manager said.
"I also owe them something because I've become the Milan coach who has lost the most derby games in a calendar year, but we will do everything in our power to make sure this season can still be a very positive campaign."
"I think it will be very emotional to come up against Sandro Tonali, I'll give him a big hug. Sandro was an important player during our time together, we won trophies together," Pioli said.
"It will be very emotional for him to come back to the San Siro, and we wish him all the best, but from matchday two onwards."