Milan were beaten 5-1 by Manchester City in a friendly on Sunday after previously losing 3-0 to Olympiacos and Inzaghi realises they still have a lot of work to do before the start of the new league season.
"It’s in front of everybody’s eyes that we have to improve in lots of areas. We’ve not been working long and we're coming off the back of an eighth-place finish. We have to work a great deal," Inzaghi told the official Milan website.
"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. I expect more when we don’t have possession.
"Work is the only thing that will allow us to be competitive soon. It’s down to me to watch the match again and ask for more from everybody. I think that once we’re a complete group we can be competitive in the league.
"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. We have to concede fewer goals. We must improve on this aspect."
Inzaghi was recently named new Milan coach after Clarence Seedorf was sacked at the end of the 2013-14 campaign.