A Jeremy Menez brace plus a goal to Cristian Zaccardo helped them to a 3-1 win over Parma at San Siro.
Philippe Mexes (suspension), Stephan El Shaarawy (broken metatarsal) and Nigel de Jong (hamstring) were among those missing for Inzaghi's men on Sunday.
And the Milan boss said it was crucial to get the three points, and hoped he could gain some reinforcements ahead of their trip to leaders Juventus on Saturday.
"This was a complicated game, as I knew it would be with eight or nine absentees. At the moment we are getting negative results as well as injuries," Inzaghi told Sky Sport Italia.
"We wanted this victory at all costs, I think it is deserved and now we hope to get some players back for Saturday. We then also hope to play a little better as time goes on.
"When you are without seven or eight first choice players and coming off a difficult period, it becomes tricky."
Veteran defender Zaccardo deserved his goal, Inzaghi said, in what was the former Parma man's first league game of the season.
"Zaccardo never played this season, but always trained hard and today not only did well, but also got a goal," Inzaghi said.
"This attitude is what I expected from the squad.
"We must get back to being the team that got results against Juve, Roma and Napoli."
In the 74th minute, Inzaghi withdrew loan signing and striker Mattia Destro, and brought on defensive midfielder Sulley Muntari - and said he understood why the crowd jeered at the negative tactic.
"It's only normal that people want more, we all do, but I think the fans will be happy with the hunger they saw tonight. As the banner requested, 11 lions," he said.
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