Despite taking the lead thanks to Tom Lees early on, first half goals from Sam Surridge and Ryan Yates handed the home side the victory.
This means it will be Forest that will host Liverpool later this month following their previous cup wins over Arsenal and Leicester.
Huddersfield can now focus on winning promotion from the Championship - currently sitting in second place ahead of their trip to The Hawthorns on Friday night.
West Brom picked up their first win since Steve Bruce’s arrival at the weekend and have majorly dropped off in the race for a play-off spot.
Here are the best of today’s transfer rumours...
1. West Ham targeting Nottingham Forest ace
West Ham are continuing to keep a close eye on Nottingham Forest centre-back Joe Worrall ahead of the summer. David Moyes has found success in buying from the Championship previously, with Jarrod Bowen and Said Benrahma both impressing. (Claret & Hugh)
2. Blackburn monitoring young National League forward
Blackburn Rovers are reportedly keen on signing Guiseley striker Josh Stones, with Wigan Athletic also eyeing a move. The 18-year-old signed his first professional contract with the club in October. (Football League World)
3. Ex-Leicester City defender has contract terminated
Bristol City have terminated the contract of defender Danny Simpson, with the former Leicester and Newcastle right-back falling out of favour at Ashton Gate. The 35-year-old hasn't made an appearance for the Robins since October. (Bristol World)
4. Leeds United target signs new contract
Coventry City forward Gustavo Hamer has signed a new deal with the Championship Club amid interest from Leeds United. The 24-year-old has three goals and six assists in the league this season. (Coventry City)