The Colombian defender believes the Rossoneri could have recorded a good result had they taken their chances
Goals from Lionel Messi and Sergio Busquets saw Barca grab a two-goal lead before a Gerard Pique own-goal in the closing stages of the first half helped Milan back in the game.
However, another Messi strike after the break proved to be too much for the Rossoneri as they left Camp Nou empty-handed.
"I'm not sure that there was really that much difference between the two teams tonight," Zapata told the official Uefa website.
"We went out to win here and we had opportunities to score, we just didn't convert. Despite all that we don't leave here happy.
"The match was there for the taking right until the closing stages but the goal to bring us a draw just wouldn't come our way."
Milan currently sit second in Group H with five points from four games, leading third-placed Ajax by one point and rock-bottom Celtic by two points.