It needed a stoppage-time equaliser from Jordan Hugill to earn a 1-1 draw after Richard Wood had given the visitors a 77th minute lead from the penalty spot.
In the closing stages, Paul Gallagher had a shot cleared off the line, while Adam Reach had the ball in the net only to see it ruled out for offside – a replay showed he was onside.
The Lilywhites got their rewards though, when substitute Hugill netted from close in.
Grayson said: “It was a deserved draw from our point of view, we at least deserved that.
“Overall, I thought we played well.
“The performance again probably epitomised what we have been this season.
“Leeds didn’t really look like scoring too often, we kept possession of the ball quite well but we weren’t quite ruthless enough in their 18-yard box.
“We shot when we should have passed, we passed when we should have shot, that has been the story of our season at times.
“The lads showed their character by getting a late goal again.
“Some teams might have accepted losing the last game of the season 1-0 but not my players, they kept going until the very end and got what they deserved.
“We had the better chances and Adam Reach was onside for the one which was disallowed.
“I have seen the replay of it and quite clearly he is on.
“I’m not going to lambast the officials because it is not an easy job.”
North End finished 11th in the Championship with 62 points.
Grayson said: “I’m delighted with how the season has gone.
“I told the players in dressing room after the game that they can be very pleased and proud of what they have done.
“They have put everything in both in games and during every training session.
“We know our strengths, we know our weaknesses and to finish where we have – above a lot of more experienced teams – speaks volumes for the players.”