Quickfire goals from Adam Forshaw and Marcello Trotta midway through the first half did the bulk of the damage, with Sam Saunders adding a third after the break after Joel Garner missed a penalty for the hosts.
The result extended Brentford's unbeaten sequence in League One to 10 games and means they continue to breath down the necks of the division's pace-setters.
"I am disappointed that we lost the game and conceded three goals and have not scored any," said Grayson. "They got the penalty decision and the goal straight after so I'm disappointed to go in two-nil down, there was not much in it.
"I asked for a reaction from the players - to get amongst them and win their individual battles and show more quality - and the next goal was going to be a big part of it.
"It was a great opportunity for Joel (Garner) to put the penalty away and Kevin (Davies) had a chance with the header and we had the momentum really going then. Unfortunately they got the third goal that killed the game off.
"We knew it was a tough game but too many of our players lost their individual battles all over the pitch and we did not have the right quality at times and we made wrong decisions."
Preston looked lively on the break but it was Brentford that went ahead from the penalty spot in the 23rd minute.
Clayton Donaldson latched onto a long ball and goalkeeper Declan Rudd raced out from the Lilywhites' goal bringing the striker down. Forshaw coolly dispatched the spot-kick and then set up the Bees' second goal shortly afterwards.
A slick passing move after 26 minutes allowed Forshaw a shot on goal that was parried by Rudd but the former Everton player hooked the ball back to Trotta who blasted home.
Preston were rewarded with a penalty after the break when Jake Bidwell was adjudged to have pushed Joel Garner inside the box. David Button saved the spot kick, diving to his right.
Kevin Davies could have scored moments later but he sent his free header across the face of the goal and wide.
Substitute Saunders killed the game off in the 73rd minute to extend Brentford's unbeaten run and end the Preston fightback.
Brentford manager Mark Warburton felt self belief played a big part in the victory.
He said: "I think it sends out a powerful message, it is not an arrogant one that we have come here and done a good job and the boys have got a self belief now.
"That is the key for me. We know about them technically, tactically and physically and they are in good shape. But can they believe in themselves? I think that it is getting the head right.
"We thought to ourselves what problems do they pose and we saw the wing-backs going forward but there was space behind with three defenders and they were vulnerable, in our opinion, and that is really what we tried to do and hopefully that worked out very well for us.
"If you fall beneath your standards you run the risk of losing your shirt. It is a squad game and we entirely rely on the squad it is very important to highlight that point."