The Railwaymen won comfortably with goals from David Vaughan, Ryan Lowe and Nicky Maynard as the Bees miserable season came to a sorry conclusion at Gresty Road.
Fitzgerald's team are stranded 13 points from safety with only four games to play. But the former Wimbledon player, who replaced Leroy Rosenior in the Griffin Park hotseat last November, promised his under-achieving troops would be put through their paces in the remaining weeks of the season.
"I don't think these players are good enough and I take some of the responsibility as I brought some of those players into the club," revealed Fitzgerald.
"This is the first time I have been relegated in my career and I am gutted. But if the players think they can just come in and go through the motions in the last month then they are mistaken.
"They are going to work as hard as they have ever done in their lives and I will have them in tomorrow."
Brentford's players looked like they had almost thrown the towel in long before the final whistle as they allowed Crewe to steam forward. Vaughan turned and curled in the opener in the 17th minute after some good play by Rodney Jack.
Then Bees keeper Stuart Nelson woefully allowed Lowe's angled drive to flash through his hands after the Crewe centre-forward had followed in with his own corner kick.
Darren Moss was harshly adjudged to have hand-balled as he attempted a back-pass to his keeper Ben Williams, Kevin O'Connor fired the resulting spot-kick high into the net to hand the Londoners a life-line of sorts.
But Maynard quickly restored Crewe's two-goal advantage with a super looping header from a pinpoint cross from Lowe.