Billy Davies again made a number of changes to his starting XI and saw Matt Derbyshire put Forest in front on 24 minutes.
An entertaining all-Championship clash swung in Burnley's favour with a double strike from Ings, the first coming on the stroke of half-time.
And it was the Clarets who held on to reach the last sixteen on the competition.
For Forest, attention turns immediately to Saturday's big East Midlands clash with Derby County at the City Ground.
Source: Forest MAD