The 46-year-old has spent spells as first-team coach, caretaker manager as well as a coaching role but financial constraints meant Crawley could not afford to keep Brewster.
Chief executive Richard Low told Crawley News: "As our supporters know, we are in the process of restructuring our operations and we worked hard to try and keep Craig within the financial structures which now apply to our football management but it was just not possible despite both parties' best efforts."
Brewster added: "I have had two great years at Crawley Town and being a part of the club which won promotion to League One and then established itself at this level has been one of the highlights of my career.
"I have made some great friends at the club and I wish Crawley Town all the best for the future. The club will always have a special place in my heart."