The Dutchman announced that he will depart at the end of the season due to family reasons.
Krol's decision came shortly after Zamalek learned that they will meet arch-rivals Ahli in July in the CAF Champions League group stage.
That’s why Abbas emphasized the need of a new boss sooner rather than later.
"We are in trouble now. Krol's decision came at a critical time," the wealthy chairman said.
"Zamalek need to appoint a new manager before the first of June to give him an adequate time to prepare for the important encounter against Ahli."
Krol is set to leave Zamalek following the Egyptian Cup final against ENPPI on May 25th.
Zamalek were drawn in Group A of the Champions League along with Ahli, Ivory Coast's ASEC Mimosas and Dynamos of Zimbabwe.