Milan have only won once this season and find themselves already 10 points behind leaders Roma after just five games.
They prepare for a home clash with struggling Sampdoria without talisman Mario Balotelli and the pressure is starting to build on Matri to fill the void.
He has yet to break his duck since a move from Juventus, but his side's defending is more of a concern for Allegri.
"We have got to improve in defence, but also in attack, seeing as we only convert about 30 per cent of our scoring opportunities," he said.
"Matri played for the team and I hope he can break his duck on Saturday. If he continues like this, the goal will come."
Milan are the comeback kings in Serie A this season, they have scored late goals in three of their five matches – earning them points in two of them.
Sampdoria are struggling under Delio Rossi and have yet to taste victory in this campaign, their two draws – which have both come away from home - leave them on two points and in the bottom three.
They will take heart from the fact that they were unbeaten against Milan last season and won at the San Siro thanks to a Junior Costa goal.
Balotelli will serve the second of his three-match ban, while Kaka (thigh), Mattia De Sciglio and Giampaolo Pazzini (both knee) are all definitely out through injury.
Allegri also has doubts over Riccardo Montolivo, Stephan El Shaarawy (both thigh) and Daniele Bonera but the latter may not be risked as he continues his recovery from a knee injury.
The visitors have concerns of striker Eder and Daniele Gastaldello (both knee) but will hope to have them for their trip north.
