Reading's victory at Doncaster Rovers means that Bournemouth are four shy of the top six with one game to go, with today's braces from strikers Yann Kermorgant and Lewis Grabban not as sweet as they might have been.
The Cherries started on the front foot this afternoon and went close twice in the first 10 minutes.
Forest, whose own hopes of reaching the playoffs are now also over, had a decent spell towards the end of the first half and Matt Derbyshire could have slotted them in front, but he fired straight at Lee Camp.
Kermorgant was the one to open the scoring five minutes before half time when he met Simon Francis's cross from the right.
It was two soon after half time when Grabban slammed home a loose ball after Eunan O'Kane's burst into the box.
Three became four in stoppage time as Kermorgant got in on the act again with a powerful finish after being teed up by Tokelo Rantie.