Goals from Alan Judge and Marcello Trotta added to an early Aden Flint own goal before the break as the Londoners took control of a one-sided affair.
Robins defender Flint gave the hosts the perfect start inside 10 minutes when he bundled Jake Bidwell's left-wing cross into his own net.
"That rocked us on our heels," said Cotterill. "I was very disappointed to give them a goal against the run of play.
"We seem to have an unhappy knack of giving sides a goal start and then having to fight our way back into the game, but when you give away another two soft goals it makes it a mountain to climb against such a good side."
Cotterill dismissed the second half, during which Brentford rarely moved through the gears, as a "nonentity" and admitted Brentford were good value for the points.
"They are in the habit of winning and we have been used to losing. It's a habit we need to get out of by being mentally stronger," Cotterill added.
Former Brentford defender Karleigh Osborne gave Cotterill a glimmer of hope two minutes after the opener, firing across Bees goalkeeper David Button into the far corner before immediately limping off with a hamstring injury.
Tyrone Barnett should have given the visitors the lead minutes later, but volleyed wide from close range with the goal at his mercy.
On-loan Blackburn midfielder Alan Judge made City pay midway through the first half when his blistering drive from 12 yards after a slick counter attack was too hot for goalkeeper Elliot Parish to handle.
Marcello Trotta made it three just before the break, sweeping home Judge's low cross before the home side shut up shop after the break, the only noteworthy chance falling to Barnett, whose rising drive flew over.