The Clarets went back to the top of the Championship with the 1-0 victory at Deepdale, Joey Barton’s free-kick deflecting off Alan Browne in the PNE wall for the only goal.
That came in the sixth minute and both sides had chances to add to the scoreline, Andre Gray and George Boyd hitting the woodwork within seconds of each other in the second half.
North End finished strongly but as has been the case a number of times this season, the final ball often lacked quality.
Daniel Johnson forced a save from Burnley keeper Tom Heaton, while Callum Robinson was inches too high with a stoppage-time chance.
Lilywhites boss Grayson said: “I was disappointed that we lost the game but was pleased with the performance of the players.
“Burnley knew that they had been in a game and had to work for their result.
“Our performance was very much like we have been all season, we worked extremely hard, defended well and put bodies on the line.
“In the second half we asked questions of them but maybe where it mattered in the final third we didn’t have that extra bit of quality - that comes with budgets.”
Burnley were certainly one of the best organised sides to have visited Preston this season.
Their defence held firm throughout, Jermaine Beckford carrying PNE’s biggest threat against them as he came through 90 minutes for the first time since his knee operation.
“Burnley are a very strong, organised team, they know what they are doing,” said Grayson. “I’m not saying they have the best individual players but they are one of the best teams because of how they work, their recovery runs and they know how to manage games.
“They have players who can influence it. We are a bit away from them because we have come from League One and they have been in the Premier League.
“While we are disappointed to have lost, we asked questions of them and did well, like we did at Middlesbrough a couple of weeks ago.”
North End lost Ben Pearson to an ankle injury after 10 minutes, meaning an early bow from the bench for Johnson.
Later in the first half, Grayson switched formations from 3-5-2 to match Burnley’s 4-4-2.
Said Grayson: “We changed it after 20 minutes or so, going to 4-4-2 from the three at the back. Burnley worked hard to limit us in terms of opportunities but we still had some half-decent ones.
“Ultimately, we have been beaten by a deflected free-kick.
“It hit Alan Browne on the head and spun away from Chris Kirkland.”