Allegri has overseen just one Serie A victory from five matches in the new campaign, a 3-1 triumph over Cagliari at the beginning of September.
Milan have had to rely on last-gasp goals to avoid defeat in recent weeks with a 2-2 draw against Torino sealed at the death, while another unlikely comeback was completed against Bologna on Wednesday.
Andrea Poli put Milan ahead, but a Diego Laxalt double and a strike from Jonathan Cristaldo looked to have handed the home side a 3-1 win.
However, Robinho halved the deficit in the last minute of normal of play, before Ignazio Abate secured a point in injury time.
The result leaves Milan 12th in the table, already 10 points adrift of leaders Roma and eight away from a UEFA Champions League spot.
But Allegri believes the side will have improved their position by the turn of the year, having hit form at a similar time last term, and hopes to start the revival by beating Sampdoria at San Siro on Saturday.
"I'll look at the league table at Christmas," he said. "In my opinion, we will be in a different position by then.
"We're a bit behind, but there are still so many games left. Let's just think about winning tomorrow.
"We have a difficult game tomorrow. Delio Rossi is an excellent coach and Sampdoria are coming off the back of a good display. But we have to win."
Allegri also moved to quieten talk about Mario Balotelli's dismissal against Napoli last weekend for confronting match official Luca Banti after the 2-1 loss at Stadio San Paolo.
"His dismissal happened six days ago," the 46-year-old added. "I think we need to stop talking about it now.
"He's said sorry and now he needs to think about working. He needs to improve the way he reacts on the pitch. He knows that and I hope he understands that."
