A late goal from Leigertwood sparked scenes of jubilation at the Madejski Stadium but Forest pushed their hosts all the way, creating the best of the chances.
Coventry's home defeat at the hands of Millwall made the final result academic from the Reds' point of view and Steve Cotterill can say job done, with his brief of keeping them up fulfilled.
While acknowledging the 'massive achievement' of his side after the game, Cotterill was disappointed not to have taken a point.
"I don't think we deserved to lose," he said.
"From 70 minutes onwards I thought we looked the better team and were going to win the game.
"It's a measure of how far we have come as a team in recent weeks is that we were on the road to (League) One and now after playing the top team in the league the lads are sitting in the dressing room disappointed that we didn't win the game."