The Rossonero won 2-0 thanks to goals from Strahinja Pavlovic and Rafael Leao in the final five minutes.
Allegri said afterwards: "Cremonese are a difficult team to play against. In the first half, they played at a very high tempo, and we struggled with possession.
"(Pervis) Estupinan came on very well, proving I have an extraordinary squad. Winning today was especially important to erase the defeat against Parma, get closer to our goal, and prepare for the derby."
He added, "It seems short because you get out of breath, but in those moments you have to stay calm: they did well from the corner and on the counterattack to close it out.
"Now we have a week to prepare for this wonderful match."
Allegri was referring to the Milan derby next week.
He also said: "The derby is a wonderful match where anything can happen. Let's hope the numbers work for us on Sunday."