The Rossoneri were 2-1 down at the break and despite a number of openings in the second half it was Barca who scored the decisive fourth goal late on.
Zapata said that with a little more composure in front of goal Milan would be celebrating a deserved point.
"I'm not sure that there was really that much difference between the two teams tonight," UEFA.com quotes Zapata as saying. "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 are currently second in the group with five points from a possible 12.