The Hammers 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 Sherwood placed in charge.
And Sam Allardyce's men completed a second successive win at White Hart Lane with a come-from-behind 2-1 triumph to set up a League Cup semi-final with Manchester City.
Spurs are out of the competition and without a permanent boss, but Sherwood suggested he would be keen on the role despite not yet being informed by chairman Daniel Levy if he will be in charge of Sunday's match with Southampton.
"The immediate future is up in the air, that's as much as I know," said Sherwood, who was due to take the development team for training on Monday morning before receiving a call from Levy instructing him to take charge of the first-team instead.
Asked if he would like the job, Sherwood said: "It would have to be right for me and right for the football club. There are a lot of big names being bandied about to take this job.
"I think the chairman and the football club need to make the correct decision and find the manager who's best compatible to take this football club forward.
"I've got to be in the frame, but it's not my decision, unfortunately."
Reflecting on the last 48 hours, former Spurs captain Sherwood, who has never before managed a team, said: "It's madness.
"I'm up for a challenge. I always have been. I'm very opinionated.
"I know a certain way I need to play. I think I can manage men and deal with them and be honest with them.
"That decision going on is out of my hands, unfortunately."
Sherwood admitted Spurs' confidence is fragile.
He said: "The confidence is low. It takes a battering when you lose a few games, but it's up to whoever's in charge on Sunday and training on Friday to get them prepared.
"If it's me I certainly won't be going in all doom and gloom. You need to lift these guys and we have to go and get a result for the football club."
Nevertheless Sherwood paid tribute to Villas-Boas.
He added: "I think he did a good job at the football club as a whole. I wish him well. He's a really nice guy and everyone liked him around the football club.
"It's the decision the club decided to make and we all have to abide by it."
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 to send the Hammers, struggling in the Premier League, into the semi-finals.
The Hammers, who had won just two of the 10 matches between visits to White Hart Lane, had been blunt until exposing the defensive deficiencies which were all too evident all too often during Villas-Boas' reign, including in Sunday's 5-0 home loss to Liverpool.
Sherwood added: "It's a major disappointment to the lads in there. They're absolutely sick in there and so am I.
"They ran out of a bit of steam. I think they're fit enough, (but) it's a complete change of mindset of how I've asked them to play.
"I've asked them to go a little bit more gung ho and up-and-at-em and you need to acclimatise to that."
Adebayor was making his first start of the season and scored his first goal since May after a rumoured fallout with Villas-Boas.
Sherwood added: "He's not got a point to prove to the fans. You could see the way they reacted to him.
"If he shows that effort and drive, which he did tonight, and a real desire to want to play, I've got no hesitation to have him around the team."
West Ham boss Sam Allardyce hopes the win can provide a much-needed fillip for his relegation-threatened side.
"It was a fantastic victory for us," Allardyce said.
"It's a brilliant effort from the squad today. 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."
The defeat for Tottenham was compounded by a hamstring injury for Andros Townsend, who could be out until the new year.
"It doesn't look good," Sherwood said.