The coach was encouraged by his side's performance against Liverpool but admits they must shed the "anxiety" of last season if they are to improve results
Goals from Joe Allen and Suso secured a victory for Brendan Rodgers' side despite Milan enjoying strong spells for much of the match, particularly in the second half.
The result brings to an end a dismal run of pre-season games in America in which the Rossoneri also lost 5-1 to Manchester City and 3-0 to Olympiakos, but their coach was encouraged by the improvements he saw within the performance.
"I'm sorry for the result, but it was the response I was expecting. There was a good reaction. I don't remember our goalkeeper making a save, whereas Simon Mignolet was called into action," he told the club's official website.
"We have to continue with this spirit and desire. For the lads, I can only say that we must continue, and when we face teams in Italy our character will come out.
"We conceded two goals when we had possession, but I am the one asking them to play from the back. We are Milan and we can't just fire the ball up field. Perhaps we are a bit naive.
"While in the other games we struggled, here we played on a par with one of the best teams in Europe.
"We're starting to see traces of the Milan I want, especially in terms of determination. There is a good spirit and we have to work from there.
"This team needs to shake off some of the fear and anxiety from last season and I think this game can help give a lot of confidence."
M'Baye Niang was a positive spark for Milan, causing a real handful for the Liverpool defence from his wide position, and Inzaghi believes the Frenchman could become a top-class player if he is allowed time to develop properly.
"Niang is doing well, he has a good attitude and I don't think there are many players born in December 1994 who are this good. We need to give him time and confidence," he added.