Lamptey and Barcelona loanee Fati went down injured in the first half of Brighton's 3-2 victory at Nottingham Forest on Saturday when they ended their six-game winless run in the Premier League.
Brighton, who face AEK Athens in the Europa League later on Thursday, have been struggling with a number of key players out of action, including Kaoru Mitoma, Danny Welbeck, Solly March and Julio Enciso.
"Ansu and Lamptey are both injured," Italian De Zerbi told reporters on Wednesday.
"We have lost them for a long time, I think."
Brighton are second in Group B on seven points from four games, a point behind Marseille. They lost to AEK in their campaign opener but have the chance to make up for that defeat in Athens.
The lengthy injury list makes their task harder but De Zerbi said they had to focus on the players who are fit.
"We will have to compete," he added. "I don't know if we will win, but we will fight to win the game for sure."
