West Ham reached the last four of the competition with an excellent come-from-behind win that ruined Tim Sherwood's first match in charge of Tottenham.
Sherwood – appointed as the club's caretaker manager after Andre Villas-Boas was sacked on Monday – saw his side take a deserved lead with 23 minutes to play when Emmanuel Adebayor scored in his first start this season.
West Ham produced an excellent response, though, testing Tottenham goalkeeper Hugo Lloris on three occasions before Matt Jarvis fired in an equaliser with 10 minutes left.
And substitute Modibo Maiga headed home the winner in the 85th minute, with his first goal in more than a year sealing their progression.
"(The team's mindset was that) we were going to give Tottenham a really good game and really that's all they've done," Allardyce told Sky Sports.
"They've gone out there and tried their hardest and it has paid dividends. Tactically we got it right, we were patient, we waited.
"The fact they scored from our corner was disappointing but the response was fantastic.
"After we went 1-0 down, we were the better side and ultimately got our reward with a 2-1 win."
Allardyce's side will travel to Manchester City for their semi-final in January.
West Ham have never won the League Cup, losing finals in 1966 and 1981.
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