An inspired second-half performance from the Blades was enough to force extra time after they fell behind in the first period thanks to Brennan Johnson’s goal, but Forest goalkeeper Brice Samba saved three penalties in the shootout to send his side to Wembley.
Goals from Morgan Gibbs-White and John Fleck gave Paul Heckingbottom’s side a 2-1 win on the night, which levelled the scores at 3-3 overall.
Samba saved from Ollie Norwood, Conor Hourihane and Gibbs-White, with Sander Berge and Iliman Ndiaye converting their spot kicks.
Brennan Johnson, Steve Cook and Cafu scored for the home side, but Joe Lolley blazed his effort over the bar.
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9. Ollie Norwood - 7
A considerably better display than Saturday. Used his ability to find a teammate to good effect and start United's attacks and produced several brilliant tackles. Photo: Andrew Yates
10. Sander Berge - 7
Found Gibbs-White for the goal with some nice footwork and a cutback from the byline. Used his aerial presence to good effect. Photo: Simon Bellis
11. Morgan Gibbs-White - 7
Showed great vision to find Ndiaye early on, who saw a golden opportunity saved by Samba. United's liveliest attacker on the night and poked home to level the scores at 1-1. Photo: Simon Bellis
12. Iliman Ndiaye - 7
Like the rest of his teammates, improved as the game wore on. Saw a great chance to open the scoring saved by Brice Samba from point-blank range in the first half but involved in both goals and saw a late effort well saved by Samba. Photo: Simon Bellis