A Clayton Donaldson brace ensured the Bees took three deserved points and claimed the psychological advantage ahead of the sides' Johnstone's Paint Trophy clash on Tuesday.
"We looked well below par for 45 minutes but I suppose you can understand blip a after the season we have had so far," Barker said.
"In a way we've built a rod for our own back with some really good away wins, but if we expected to come here and roll Brentford over then this was a reality check for all of us."
Crawley threatened only a handful of times against a buoyant Brentford side who have been creating, but not taking, their chances this season.
A defensive blunder from Bees right-back Shaleum Logan handed Crawley a route back into a game, his wayward back pass dropping for former Bee Nicky Adams to bundle home from close range.