On-loan from West Ham, Fullkrug proved the matchwinner on Sunday in their 1-0 win against Lecce.
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Allegri said: "The best thing about tonight was seeing an attacking Milan, but also good at preventing attacks in defence.
"I'm satisfied; the lads are doing well. Now, however, we have three important and difficult away games ahead of us, in Roma, Bologna, and Pisa.
"Niclas is a guy with incredible enthusiasm, it's very important for us to have a guy like him at our disposal."