After losing 3-0 to Olympiacos and 5-1 to City in their opening two International Champions Cup games, Milan finished the pre-season tournament in the United States with another reverse to Brendan Rodgers' men in Charlotte.
Goals from Joe Allen and Suso gave Liverpool the spoils at the Bank of America Stadium as the Premier League side booked their place in the final with Manchester United.
Milan's poor performances in the United States are only likely to increase the pressure on Inzaghi to deliver in his first season in charge after an eighth-place finish in 2013-14 that saw Clarence Seedorf - who took over from Massimiliano Allegri in January - relieved of his duties in June.
But the 40-year-old feels Milan displayed improvements against Liverpool and has urged his players to maintain the same spirit ahead of their season opener with Lazio on August 31.
"I'm sorry about the undeserved 2-0, but it was the response that I was expecting," Inzaghi said.
"There was a great reaction today, I'm happy with my players, I can't remember a save made by our goalkeeper whereas we worked their goalkeeper. We had a quality half an hour in the second half and the second goal is harsh on us.
"We must continue with this spirit and this desire. I can only ask my players to continue like this and then our values will come to the surface when we face sides in Italy.
"Perhaps we're still a bit naive. We conceded two goals while in possession, but I'm the one to ask the side to play from the back, we're Milan and we can't throw the ball away.
"We'll move forwards for now but the reaction from everybody in the defensive phase pleases me. If it had ended 1-0 or 1-1 there would be no complaints. We were up to the standard and this has to be a starting point for the next matches."
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