Jermaine Beckford headed home two minutes from time to seemingly level the scores and set up a grandstand finale at Deepdale.
PNE were left frustrated however when the linesman’s flag went up, the Cottagers ultimately holding on for victory.
Grayson said: “It’s definitely onside.
“Tom Clarke is onside and heads it back where Jermaine has probably got two or three players in front of him.
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“Tom’s more or less headed it behind as well so he can’t be offside.
“It’s a clear onside. Supporters aren’t daft either. When you see the supporters all round that side jumping up and down saying it was onside you’ve got to sometimes go with it.
“And I thought in real time it looked a clear goal.
“We’ve not got the breaks but you can’t use that as an excuse, we need to dust ourselves down and go again on Tuesday (against Derby at Deepdale).”
As on the opening day at Reading, North End were left chasing the game, Sone Aluko and Matt Smith giving the visitors a two-goal advantage before Callum Robinson reignited the home side’s hopes with a fine header 20 minutes from time.
Grayson said: “When you go 2-0 down it’s obviously a difficult scoreline to come back from.
“We certainly made Fulham work for the win in the second half.
“In the first half I didn’t think there was much in the game, they probably looked a little bit more threatening going forward given the pace that they had in the team.
“It was a disappointing goal that we gave away, Browney clears it straight against their lad and they score.
“Second half I thought we were better and then it was a bad goal to give away, three of the lads should have made challenges.
“We’re then 2-0 down but there’s character in the group and we got the goal and were taking the game to them and had a perfectly good goal disallowed for offside.
“It’s disappointing, there are positives from the game but ultimately we have to be better all round if we can.”