The Clarets recovered from a nightmare start to draw 1-1, having conceded to a Neco Williams goal after just two minutes on the clock.
But Scott Parker’s side fought back well and levelled through Jaidon Anthony, who netted for the third time this season already.
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Burnley were the stronger side at the start of the second-half and had chances to edge their noses in front, but were unable to find that killer touch.
Ange Postecoglou’s side ended the game the stronger, but they found Martin Dubravka in inspired form in the Burnley goal.
Here’s how Burnley’s players rated:
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5. Maxime Esteve - 8/10
A colossus. Made some crucial interceptions, but otherwise breezed through the game without being particularly stretched. (Photo by Matt McNulty/Getty Images) Photo: Matt McNulty
6. Quilindschy Hartman - 8/10
Got up and down the left flank well and often left in acres of space. Made a crucial block to deny Forest a late winner and tested the Forest keeper with an ambitious long-range effort (Photo by George Wood/Getty Images) Photo: George Wood
7. Josh Cullen - 8/10
Swept up well, picking up the bits and pieces, and always took care of the ball in possession. Just couldn't get out to Neco Williams quickly enough for Forest's goal (Photo by Matt McNulty/Getty Images) Photo: Matt McNulty
8. Florentino Luis - 7/10
Had to be careful after picking up an early booking for a late challenge, which looked a little harsh. Meant he wasn't quite as combative as we saw last week (Photo by Nigel Roddis/Getty Images) Photo: Nigel Roddis