A poor 2013-14 campaign and a torrid pre-season have not filled Rossoneri fans with confidence but the defender has faith in returning to Champions League football
Filippo Inzaghi's first test as Milan coach saw him steer the Serie A club to three losses at the International Champions Cup - a pre-season friendly tournament that pitted them against Olympiakos, Manchester City and Liverpool.
Milan scored just once - against City - while shipping 10 goals, as their bid for a fresh start on the back of last season's eighth-place finish in Serie A failed to gain any momentum.
With their season opener against Lazio on August 31 edging closer, Zapata insists that the Rossoneri's aims have not changed regardless of the poor US tour results.
"Let's hope that this year things can go better. We want to finish as high as we possibly can, the target is to get into the top three," the Colombian told the club's official website.
"We are working to create a good group, that's what Inzaghi is working towards. We need to be ready for the start of the season.
"The boss looks you in the eye when he talks to you and that is important. He is giving confidence to everyone and that is vital for a player.
"I'm pleased with how preparation is going. I am very motivated to have a great season with Milan. I put a lot of faith in this shirt. We are trying to take Milan as high as we can."