Zola admits the decision for him to front the media was made by Maurizio Sarri, who was sent off in the closing moments, as he had "a lot of emotion" but explained what the cause of the dispute was.
"It is a football game and there is a lot of passion," Zola told Sky Sports.
"We are not happy because of the result and we are not happy because he didn't play enough and of course we showed all our emotions because we care, they did the same.
"Paolo Bertelli isn't happy because of some words that were said to him, we will follow on that.
"The rest you cannot expect that we do a game like this - it was a big game for us and we cannot go in like nothing happened."
Zola continued to the BBC: "Sarri was very upset because he has heard not good words towards him from the Burnley bench.
"The only reason he walked over there was to get our players to go into position, he was trying to help the ref. Kevin [Friend] misinterpreted. I'm disappointed, he wanted to help him."
Zola added: "We wanted to win. They didn't want to lose.
"We are unhappy. There was too much time wasting. Five minutes injury time wasn't enough to compensate. We couldn't build important rhythm.
"We were hoping for something more. We are determined to fight until the end. This team are playing good football. We need to improve but we're in a good way. We care as we showed today.
"We expected it to be a tough game. We didn't expect so much time wasting. We expected Kevin [Friend, referee] to give more extra time. That's why we're very unhappy."