The 18-time Serie A winners find themselves five points clear of the bottom three as they prepare to return from their mid-season break, and Allegri knows they have to improve quickly.
With only four wins in the league this season Milan are in danger of their worst finish since 1981-82, when they were relegated, and have signed Keisuke Honda and Adil Rami to try and turn their fortunes around.
Atalanta may have only beaten Milan once in their last eight meetings but Allegri knows it will be a tough task at San Siro on Monday.
"Atalanta are very organised and doing well this season," he said. "It's an important game and we mustn't forget we have only 19 points.
"We need to look over our shoulders, as this is a relegation dogfight.
"We've got to start 2014 off the right way, because our table is unimpressive and we need to learn from our mistakes. We cannot afford another slip-up.
"Tomorrow we must do everything possible to win, as the next few months have got to be different from the last few. We must have the humility to acknowledge we're closer to the relegation zone than the European places."
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