Milan travelled to the Stadio Luigi Ferraris on the back of a three-match winless streak, including last week's home loss to Palermo, but they took the lead early on in Genoa through Stephan El Shaarawy's first Serie A goal since February 2013.
Sampdoria equalised on the stroke of half-time through Stefano Okaka before Eder gave them the the lead soon after the restart.
However, Jeremy Menez restored parity from the penalty spot in the 65th minute, although captain Daniele Bonera's dismissal late in the game for a second yellow card did take the shine off a valuable point for the visitors.
Nevertheless, Inzaghi was delighted with his side's spirit.
"This is Milan we have always seen, against Palermo we saw something unthinkable," he told Sky Sport Italia.
"Today I am very happy. I'm sorry because we deserved a win but a lot of strange things happened in this game, and I congratulated everyone who gave their all.
"El Shaarawy's goal was a beautiful thing. These are the matches for him to show his capabilities. Bonera? We will miss him against Inter."
