Preston remembered their favourite son with an impeccably-observed minute's silence, black armbands and 'Finney' emblazoned on the back of every Preston shirt.
Mathieu Baudry scored the opener for the visitors at Deepdale just before the interval, but Joe Garner's penalty just after the hour-mark - after Baudry was deemed to have fouled Craig Davies - earned Preston a share of the spoils.
Grayson said the club owed a determined promotion bid to the memory of all-time great Finney, who died aged 91 on Friday night.
"It was a massive shock and we should all be proud of the club for how we've organised the shirts and everything to celebrate Tom Finney's life," said Grayson.
"I had the privilege and honour to meet him last year and he played far before I was born, but you owe it to meet these people when they're connected to the club.
"We spoke about football for two or three hours and it could've been all day.
"When it's a person like Sir Tom, it's no surprise nationally and worldwide people have paid their respects. That's the mark of the man, he was a fantastic man.
"Maybe at the end of the season he'll be looking down as we do something great and maybe get promoted.
"It would be a fantastic way to do it, and we're in a position to do that.
"I thought the supporters were brilliant in hard conditions.
"People hopefully have seen where we've come in the last year and I want people to keep coming back in numbers."
Orient boss Russell Slade was fuming about the decision to award the penalty that cost his side all three points.
"We've taken the lead and Preston have equalised from a penalty situation, which I think was an excellent dive in my opinion," Slade said.
"I'm immensely unhappy with the decision and in the second half their keeper (Declan Rudd) has saved a shot outside of the penalty area - three or four yards outside - and that should've been a sending off.
"We're a threat from set-pieces which we really exploited - Baudry went close early on and then of course he put one away at the end of the first half.
"We were set up a lot better defensively and we really limited Preston to very few chances.
"Kevin Davies has had one glorious chance at the end, but apart from that they've not had a lot and I'm glad he didn't score because it wouldn't have been deserved.
"It was a difficult occasion. It was a big atmosphere and an emotional day all round.
"It was important that we got something out of the game and perhaps I'll look back on that as a decent point. But when I look at that penalty decision it's very disappointing."
- Sports & Recreation
- Tom Finney
- Mathieu Baudry
- Craig Davies