Filippo Inzaghi's first test proper 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 Olympiacos, Manchester City and Liverpool.
Milan scored just once - against City - while shipping 10 goals, as their campaign to improve on an eighth-place finish in Serie A failed to gain any momentum ahead of their season opener against Lazio on August 31.
Zapata said their aims had not changed, despite being outclassed by European opposition in the US.
"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 Milan Channel.
"We are working to create a 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 set a lot of store by this shirt. We are trying to take Milan as high as we can."
