The Hammers came from behind to claim a second successive win at White Hart Lane.
Allardyce's men won 3-0 in the Premier League encounter in October in one of the results which ultimately cost Andre Villas-Boas his job and saw Tim Sherwood placed in charge of Spurs for the League Cup quarter-final.
Sherwood thought he had made a dream start to life in the dugout when Emmanuel Adebayor put Spurs in front midway through the second half, but Matt Jarvis scored 10 minutes from time and Modibo Maiga headed in an 85th-minute winner.
That sent the Hammers, struggling in the Premier League, into the semi-finals, where they will face Manchester City.
Allardyce hopes the win can provide a much-needed fillip for his relegation-threatened side - and said: "It was a fantastic victory for us.
"It's a brilliant effort from the squad. It's a great night for us, it's a great night for the West Ham fans, because it's twice on the trot.
"It's a victory we can enjoy tonight, but tomorrow it's up and at it again and getting ready for Manchester United.
"With a resilient performance - like we showed tonight - against Manchester United, hopefully we might get something there. Hopefully it will kick us on."
It was Maiga's first goal in more than a year and Allardyce hopes it will be the start for him, too.
"I'm delighted for him because he's showed glimpses of what we saw when we watched him in France," Allardyce added.
"All I hope is it's unlocked the door for him and he goes on to continue to score more goals."
Looking ahead to the two-leg semi-final against City - the Hammers travel to the Etihad first - Allardyce said: "It's a tough one, isn't it? If it had been one leg and if it was a draw and it pulled out that it was at our place, not at theirs, it would have been nice.
"Over two legs it makes it a little bit more difficult when you know Man City have scored on average four goals every home game."