Sturrock was relieved of his duties by chairman Ron Martin on Sunday, but claimed he had already been preparing to leave the club when his contract expired at the end of the season.
Martin, who has since appointed Phil Brown at the helm, said Sturrock had "earned the privilege" of leading out the team against Crewe on 7 April and had agreed to do so.
But the Scot, 56, has now decided not to take up the League Two side's offer.
"Paul Sturrock has announced he has politely declined the chairman's offer for him to manage the team at Wembley," the club said on its official Twitter feed.
"Paul will travel with the supporters to the game and sit in amongst the fans."