Ansu Fati and Simon Adingra contributed with a goal and an assist each to help a clinical Seagulls side claim all three points and boost their hopes of progressing to the knockout rounds.
However, the victory in Amsterdam was somewhat marred by the loss of three senior figures, with Milner the first to make way after just eight minutes after sustaining a knock.
Dunk was then taken off at half time after receiving treatment on a groin problem in the closing stages of the first half, while Estupinan - returning from a five-week muscle injury layoff - lasted just 12 minutes after being brought on as a second-half substitute.
Discussing the injured trio in an interview with TNT Sports after the game, De Zerbi said: "I'm very worried about the injuries but it's a problem we are finding in this moment.
"We have a lot of injuries, especially in the full-back position. We have to find another solution, because we play Sunday another crucial game [against Sheffield United] for us and we want to win."
De Zerbi was specifically asked about whether Dunk will be available for selection against the Blades, and the Italian is hopeful that the Brighton captain has not sustained a serious injury.
"I don't know [about Dunk] at the moment," De Zerbi added. "I think it's not a big problem, but he's played so many games in a row. We have to understand better the [injury]."
Dunk, Milner and Estupinan are the latest names to join a crowed Brighton treatment room that also includes Solly March, Danny Welbeck, Tariq Lamptey, Julio Enciso and Jakub Moder.
March and Enciso are both ruled of long term with knee injuries, while Moder has been sidelined for the last 18 months with a troublesome knee problem of his own, although the midfielder has begun to build up his match fitness with the club's Under-21s.
Welbeck has missed the last four games with a muscle injury and is facing a lengthy spell on the sidelines, while Lamptey could be in a position to return after the international break if he fully recoveres from an unspecified problem.
Despite the injuries, De Zerbi was "delighted" with Brighton's victory over Ajax, which has helped them climb into second place in Group B of the Europa League, one point behind Marseille at the top and three clear of third-placed AEK Athens with two games remaining.