Sheffield United posted a 2-1 victory after 90 minutes, sending the tie into extra time after Forest had prevailed by the same scoreline in the first leg.
After extra time brought no further goals, penalties determined the winner with Forest goalkeeper Brice Samba saving three of Sheffield United's five spot kicks.
Brennan Johnson had earlier given Forest a 1-0 lead on the night, the club's top goalscorer converting smartly from 10 yards out to put the East Midlands outfit on the brink of the final.
The Blades almost won it at the end of extra time, Samba pulling off a miraculous save at point-blank range with Iliman Ndiaye seemingly set to score from eight yards.
Forest will now square off against Huddersfield Town after the Terriers edged out Luton Town on Monday night. body check tags ::