Manchester United will face Newcastle in the final on February 26 after they beat Nottingham Forest 2-0 in the semi-final second leg at Old Trafford - sealing a 5-0 aggregate win.
The foundations were laid with a 3-0 triumph at the City Ground in last week's first leg and quickfire goals in the rematch from Anthony Martial and Fred rubber-stamped their trip to the capital.
Forest had chances to make a game of it in the first half but Brennan Johnson and Emmanuel Dennis both missed and they went out with a whimper.
"We are overall disappointed we haven't got through because when you get this far you want to go one step further," said manager Steve Cooper.
"The damage was done last week and I couldn't say that before because it was a defeatist message. If we score the clear-cut chances in the first half, or even one of them, then it is a different game. United over the two legs have been far better than us.
"We shouldn't lose sight of the fact we have got to a semi-final and how many clubs would have loved to have been on the stage we have been on in the last couple of games? The first time in 30 years.
"This time last season we were 10th in the Championship, so for us to try and compete in the Premier League and get to semi-finals tells us that the club is on an upward projection."
There was a flashpoint in the second half when Johnson clashed with Alejandro Garnacho after the United winger appeared to say something inflammatory, but Cooper would not be drawn on the matter.
"Yeah, I don't want to comment on that," he said.
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