Manager Steven Gerrard says he will take the blame for Rangers' fifth successive semi-final defeat, but warned his players they must "step up".
The Ibrox side controlled large parts of the Scottish League Cup tie with Aberdeen at Hampden but could only muster one shot on target.
And they succumbed to Lewis Ferguson's late header as Aberdeen won 1-0 to set up a final against holders Celtic.
"Everything that's gone on is on me and I'll take it," Gerrard told BT Sport.
"I pick the XI, I brought in 14 players. It's a disappointed dressing room but I'm here to take responsibility - my players, my tactics, my gameplan. If there are any fingers to be pointed let them point at me.
"We got into some good positions and either made the wrong decision or showed a serious lack of quality. If these players don't step up, it's simple at a big club: the manager goes and finds better quality."
Two years ago Rangers lost in the semi-finals of both the League Cup and Scottish Cup to Celtic, who also beat their Glasgow rivals in the last four of the Scottish Cup last season, when Rangers lost to Motherwell in the League Cup semis.
Including their 3-2 defeat by Hibernian in the 2016 Scottish Cup final, Sunday was a sixth straight cup defeat at Hampden.
Rangers' performance was reminiscent of Thursday's 0-0 Europa League draw with Spartak Moscow at Ibrox, with few telling deliveries into the box despite an abundance of possession.
Gerrard acknowledged the similarities and said his side "didn't have any quality" in the final third.
"We huffed and puffed and created half-chances but that's not enough in semi-finals. People need to have the courage and responsibility to step up and take them," he said.
"We congratulate Aberdeen, they've smashed and grabbed and punished us from a set piece and they go through."
Umar Sadiq led Rangers' attack in the absence of ineligible Kyle Lafferty and suspended Alfredo Morelos, who received his second booking in the competition against Ayr United in the quarter-final.
When asked by RangersTV if he would have done anything differently, Gerrard conceded that he would not have played Morelos against Ayr.
"That's one regret that's swirling around in my head right now. I'll learn from that," he said.
"This one will be tough to move on from straight away, because of the stage, because of the opportunity that's gone by. If you've got anything about you, it should hurt for a little while."
'It's a huge blow for Gerrard' - analysis
Scotland assistant manager James McFadden on BBC Scotland's Sportscene
It's a huge blow. They're judged on winning silverware at Rangers. Gerrard knows the demands at a club of that size. He was very critical of Sadiq a few weeks back so it was a massive gamble to put him in.
It wasn't just him, but he didn't have a threat, he ran offside, he looked lost at times and his dive [in the penalty box, for which he was booked]… try and stay on your feet and get a tap-in. The quality from the wide areas wasn't there today - normally they've been good getting the ball wide and getting balls in the box.
Former Rangers forward Billy Dodds on BBC Radio Scotland's Sportsound
Rangers will be kicking themselves. They have passed the ball about well, they have got to the areas. But I thought their quality today was nothing short of woeful.
They were the dominant team but they didn't look like scoring. [Their crossing attempts] were terrible. They didn't deserve to win it because their quality was terrible.