Young Clarets beaten by Forest
The Clarets fell behind just before the half hour as Oliver Burke forced the ball in from close range from a corner.
Brad Jackson, Ntumba Massanka and Andreas Bianga went close to an equaliser before half-time, but in the second half, Forest took control and doubled their lead on 65 minutes when Tyler Walker - son of Forest legend Des - fired home.
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Hide AdThe hosts would have stretched their lead further but for an impressive display from keeper Tony Aghayere.
But two goals proved sufficient to extend Forest’s unbeaten run to 10 games and earn a home tie in the quarter-finals against either Manchester United or Tottenham Hotspur.
Burnley lined up: Tony Aghayere, Hamam El-Fitouri, Waqas Azam, Shaun Hobson, Andy Nugent, Brad Jackson, Andreas Bianga, Brandon Wilson, Christian Hill (Jamie Frost 60), Ntumba Massanka (Josh Dolling 72), Khius Metz (Jamal Crawford 76). Subs not used: Billy Grogan, Vashiko Dixon.