With the Rossoneri trailing 2-1 with 20 minutes left, Pazzini struck twice in quick succession, helping Milan complete a comeback to triumph 4-2.
Allegri has thanked Pazzini for helping his side achieve all three points in the chase for Champions League places.
He told Sky Italia: "I am happy with the performance, as we played well and with a little more sharpness in the first half could've put the game on a different level.
"Pazzini is an extraordinary player, as he moves so well in the penalty area and is a real fox in the box. I'm very happy with his brace, but the whole team played well tonight.
"I also thank the fans for the banner, which shows they examined everything I've done in my three years at Milan. At this moment we have to think about securing third place, which was considered unthinkable after the first eight rounds."
Milan currently sit a single point ahead of Fiorentina in the third and final Champions League place in Serie A.