The Colombian defender believes his boss is behind the Rossoneri's resurgence since Christmas and has underlined the importance of finishing third in Serie A
The San Siro side were struggling to find their best form in the opening stages of the 2012-13 campaign and even found themselves battling against relegation at one point.
Nevertheless, they have climbed to third spot in the Serie A table in 2013 and Zapata feels much of their revival is down to the former Cagliari coach.
"The coach has built a good team and all the credit goes to him. Allegri is very important and he has done well since coming to the club," the 26-year-old told Milan Channel.
"The one-point lead that we have over Fiorentina is important and it might become four points this weekend as they’ll be up against Roma [on Saturday] who are a great team. It’s vital we get back into the Champions League."
Milan host Torino on Sunday as they will be looking to extend their lead over the Viola.