The Colombian centre-back feels that the draw with the La Liga champions gives them a good foundation to build on for the rest of the season.
"We played well against Barcelona and that allows us to look to the future with a lot of confidence," Zapata told Milan Channel.
"We want to keep growing and continue on this path. We embarrassed ourselves against Caen, so the only way to make up for that is to train well and do as well as possible.
"We've all got to work together to emerge from this situation. I think this was clear against Udinese and Barcelona, as we are working very hard. When things go wrong, it is down to everyone, so we are all trying to resolve the problems."
Milan are currently eighth in Serie A.