Albion secured their first win in seven Premier Leagues with a 3-2 victory at City Ground on Saturday. Anthony Elanga put the hosts ahead early on, but Evan Ferguson levelled before substitute Joao Pedro's brace.
When the full-time whistle blew, De Zerbi sprinted over to Brighton's away fans instead of shaking Cooper's hand; something the Welsh manager appeared to be taken aback by.
"I have not seen him [De Zerbi]. I don't want to get into that to be fair. It is something you will have to ask him about," said Cooper. "If you ask me, I am a British coach, I have been brought up in always shaking hands after games, showing respect, and trying to win and lose with dignity. I am not saying he has not done that, you'll have to ask him.
"But if you ask me about what I will do, I will always shake hands. But I understand that maybe elsewhere it is a bit different. That is how it is."
De Zerbi said this period has been one of the "toughest" moments in his managerial career, due to Brighton trying to balance playing in the Europa League and the Premier League, plus the sheer number of injuries his side is facing.
“I want to explain our celebration, it wasn’t disrespectful to the opponent because I am used to living inside of football, but we are suffering a lot with injuries, we lost two players in the first half, we suffered a red card, we lost two points in the last games against Sheffield United and Fulham, the last win in the Premier League was at the end of September," he said.
“We are suffering a lot because it is one of the toughest times in my career. It was a big, big celebration. We are very happy and I am very proud of the character and attitude we showed in a very tough moment. Without 10 players if Brighton can compete in two competitions, seventh in the league, and in the Europa League with Ajax, AEK Athens, and Marseille, it is difficult.
“We celebrated it like the final in the Champions League, it was not the Champions League, but the way we won the game with 10 players without the captain was excellent.”