The Rossoneri unsuccessfully tried to break down their determined opponents in a result that leaves them nine points off the top of Serie A.
Carpi held AC Milan to a creditable 0-0 draw at the Stadio Alberto Braglia on Sunday as the sides produced a scrappy encounter in their first Serie A meeting.
The hosts - only promoted from the third tier of Italian football in 2013 - have already claimed a point off title-chasing Napoli this term and picked up another solid draw against a Milan attack that displayed several shortcomings going forward.
Sinisa Mihajlovic saw his side put seven goals past Sampdoria and Crotone in Serie A and the Coppa Italia in recent days following blanks against Atalanta and Juventus, but Milan was well contained by its lowly opponents, who came closest to breaking the deadlock early on.