The Robins have now lost nine of their last ten games and it looks like being a long hard winter for John Ward's men unless the manager can find someone to put the ball in the net.
Cheltenham had the better of the possession in this game and created some good chances but it was Forest that proved clinical in front of goal with midfielder Nicky Southall scoring twice in the first half.
The first goal came on 32 minutes after Cheltenham had dominated the opening half-hour.
Midfielder Dave Bird shot over the bar from only eight yards out, Damian Spencer headed wide from close range, Shane Duff placed a free header over the bar and Grant McCann forced a flying save from Forest goalkeeper Paul Smith during a good opening spell from the Robins.
But, with virtually their first notable attack of the game, Forest grabbed the lead with a well-taken goal.
Junior Agogo broke through the middle at pace before feeding Southall on the right-hand corner of the penalty area. The 34-year old wide-man took a touch before beating Shane Higgs with a fine shot just inside his far post.
Four minutes later the points were all but sealed when Neil Harris found the space to deliver a cross from the left. The ball looped over everyone including Higgs and fell to Southall at the back post, who was left with a simple tap-in.
Cheltenham kept going and sent cross after cross into the Forest penalty area during the second half only to see many of them headed out by the three-man central defence.
Smith saved with his legs from Gavin Caines and then substitute Kayode Odejayi shot wide from close range as the league leaders held firm and Cheltenham were left to ponder another 90 minutes in which they failed to find the net.