The Colombian defender has struggled to earn a place in Filippo Inzaghi's side, having dropped down the pecking order at San Siro.
However, he returned against Inter on Sunday as Milan earned a point from a 1-1 draw against their city rivals, and he is now hoping that is the start of a long run in the team.
"I hope to become a first-team regular again soon," he told Gazzetta dello Sport. "Because it's hard to find form without continuity.
"The back-line has hardly ever been the same and when you frequently change the players, it's hard to find a balance.
"I myself know that I have had some negative displays. Against Palermo for instance it all went wrong (Milan lost 2-0 and Zapata scored an own goal).
"I know that I still have a lot to prove, but I have no doubts over my qualities."
Milan face Udinese in the league this weekend looking to end a five-game winless Serie A run, something Zapata says is crucial if they are to reach their goals this season.
"We have to start winning right away," he added. "As only by winning will we get back into the Champions League.
"The derby was a missed opportunity. Not obtaining a result for Milan means lots of pressure is heaped upon us."
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