Two second-half goals from substitute Yoann Arquin, following a 54th-minute opener from Joe Colbeck, condemned Crawley to their first defeat in 14 games.
But the Red Devils can still clinch the third and final automatic promotion spot with victory over Accrington next Saturday and Brewster is demanding a much-improved display.
He confessed: "Our fans turned up expecting a good result and we let them down a bit. It was never 3-0, but the real disappointment for us was the calamity that was the first two goals that we conceded. We didn't deliver.
"We were slack and a bit sloppy against a side who are fighting for their lives. We had a few chances but could not put the ball in the net."
Crewe's late equaliser at Torquay means third-placed Crawley stay above the Gulls on goal difference, with Southend only a point behind and also in with a chance.