A Sam Vokes penalty and a late goal from Scott Arfield gave the Clarets a 2-0 victory against Rotherham United on Saturday although they were made to work hard by the struggling Millers.
Forest, without a game this weekend, make the trip to Lancashire on Tuesday night having dropped just one place in the division on Saturday.
Preston's 1-0 win against Sheffield Wednesday moved them above the Reds but Brentford, Wolves and QPR failed to do likewise.
Derby's victory at Brentford means Forest are now 11 points off a play-off place.