The second-half substitute, who had scored in his previous two midweek outings, slotted home after much-maligned goalkeeper Simon Mignolet had saved Stoke defender Marc Muniesa’s effort in sudden death.
“I was nervous, there was confusion about who would take the seventh penalty but I picked the right corner and it’s electric here now,” said Allen last night.
Reds keeper Simon Mignolet declared: “I think we deserved it, we were the better side over the two legs.”
An emotional Liverpool manager Jurgen Klopp declared afterwards: “It was great, the atmosphere was special. It was a good game for my side against a difficult side to play.
“They changed their style today. It was Butland to Crouch so it was difficult to defend. We had a few problems, but they didn’t have too many opportunities.
“Their goal was double offside but, in the end, we had luck in the penalty shootout. Over the whole 120 minutes, the players, crowd and Liverpool deserved it.
“Wembley is a cool place to play football... but we go there to win. It’s not much fun to lose.”
There was some irony the decisive moment was produced by one of the smallest players on the pitch in a match which manager Jurgen Klopp had predicted just before kick-off would be “a heading festival”.
The ball certainly saw some air time but four shots on target in 120 minutes underlined the lack of quality in the game and penalties were almost inevitable from the moment Marko Arnautovic struck a controversial offside goal in the first half.
However, Liverpool extended to 42 occasions their proud record of never having been knocked out when returning to Anfield with a first-leg lead.
Stoke fielded five outfield players at 6ft-plus to Liverpool’s two and it seemed they would target Liverpool’s weakness at set-pieces.
Former Reds striker Peter Crouch, head and shoulders above his markers at 6ft 7ins, won virtually everything in the air but Liverpool, with Lucas Leiva at the forefront, did a reasonable job of mopping up the second ball.
But the hosts were undone seconds before the interval with a move through the middle of the pitch which picked out Bojan Krkic and, with left-back Alberto Moreno nowhere to be seen, he slid a pass across to the unmarked Arnautovic who side-footed home despite replays indicating he was offside.
It was the first shot on target in the game and the sixth time in 2016 Liverpool had conceded from such.
Jon Walters and Bojan both had chances for the visitors but Liverpool, holding a 1-0 lead going into the second leg, seemed reluctant to shoot with Adam Lallana and James Milner both guilty of passing inside the penalty area, although Emre Can and Jordan Henderson had attempts from distance.
Early in the second half, Roberto Firmino forced Jack Butland to tip his shot onto the near post with his foot but Stoke quickly gained control and exerted considerable pressure, with Mamadou Sakho throwing himself at a Walters shot an example of the desperation.
Striker Christian Benteke replaced Henderson but it was Sakho who wasted a good Milner free-kick by heading wide, with Benteke failing to meet Moreno’s cross under pressure from Erik Pieters.
The hosts managed just one shot on target as the match went into extra time, where substitute Marco van Ginkel hit the post just before the end of the first period and forced Mignolet into a save in the second whereas Liverpool failed to test Butland.
Crouch and Germany international Emre Can both failed from the spot — but with Walters, Glenn Whelan, Ibrahim Afellay, Xherdan Shaqiri and Van Ginkel scoring for Stoke, and Lallana, Benteke, Firmino, Milner and Lucas on target for the hosts, Allen struck decisively after Muniesa failed.
Stoke boss Mark Hughes praised his side’s efforts. “I thought we were by far the better team. We were behind in the tie and I’m proud of what the players produced. In terms of a performance, I thought we merited a win. We got a win on paper — goodness knows how long it’s been since we won here — but the objective was to get to a Wembley final which we didn’t.”
Mignolet, Flanagan (Ibe 106), Toure (Allen 85), Sakho, Moreno, Henderson (Benteke 58), Lucas, Can, Milner, Firmino, Lallana.
Lovren, Smith, Ward, Teixeira.
Butland, Johnson,Wollscheid, Muniesa, Pieters, Whelan, Afellay, Walters, Krkic (Adam 71), Arnautovic (Shaqiri 78), Crouch, Adam (v Ginkel 98).
Bardsley, Joselu, Wilson, Haugaard.
Jon Moss (W Yorkshire).