Relegation hovered ominously into view at Deepdale by the time Graham Westley's 13-month reign came to an end in February.
Former Leeds and Huddersfield boss Grayson has overseen an upturn in fortunes and last Tuesday's victory over Oldham made mathematically sure of North End's League One status.
A 1-1 draw at Carlisle followed last weekend and Grayson wants to see 100 per cent commitment in the Lilywhites' final three games, starting with the visit of Tranmere on Saturday.
"We're safe in terms of where we are in the league but it doesn't mean to say that we take our foot off the gas because we won't," he said.
"I want to finish as high up the table and win as many games as possible and hopefully that will mean winning every game from now until the end of the season.
"The players have got a duty to do that because they're playing for their livelihoods. Just because we're safe doesn't mean to say players can go out and not perform because if they don't perform then they won't be here next year.
"That's what we'll be doing - working hard in training because our time has only just started now.
"What we do from now until the end of the season and over the summer is what sets us up for a push next year."