Inzaghi said his team had been too submissive in their International Champions Cup defeat in Pittsburgh on Sunday as City struck four times in the first half-hour before Stevan Jovetic completed his brace after the break to complete the four-goal win.
The loss was Milan's second in five days after they were stunned 3-0 by Olympiacos in Toronto and Inzaghi was disappointed with his players' work-rate.
"It's in front of everybody's eyes that we have to improve in lots of areas," the former Milan striker said.
"We've not been working long and we come off the back of an eighth-place finish. We have to work a great deal.
"We didn’t do too badly in the first 10 minutes. We did well in terms of possession and less so without the ball which we've focused less on.
"I'm disappointed because we conceded those two goals after creating chances. Without the ball we're not nasty enough, we need to react more when we lose the ball. Work is the only thing that will allow us to be competitive soon."
Milan's final International Champions Cup match will be against Liverpool on Saturday.
Inzaghi, who is in his first season as coach, conceded the onus is on him to see if he can turn his side's form around before they take on the Merseyside club.
"I'm angry with myself because if this is the performance then the blame is mine and together with my staff we'll come through it. We'll get back on track," the 40-year-old said.
"We have to concede fewer goals. We must improve on this aspect."
Milan will be looking to break back into the top three in Serie A in the coming season after dropping to eighth in 2013-14.
The famous side with the red and black stripes finished in the top three in Italy's top tier for five straight campaigns prior to their flop last term.