The former Spurs captain is yet to hear from chairman Daniel Levy if he will be in charge for Sunday's match with Southampton, but he suggested he is keen on the full-time job.
"The immediate future is up in the air, that's as much as I know," Sherwood said.
"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.
"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."
Sherwood described the 48 hours up to and including the West Ham match as "madness".
He added: "It's different. I'm not used to sleeping two hours a night and waking up thinking about footballers.
"Someone asked me the other day, I said I slept like a baby, I woke up crying four times in the night."
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.
West Ham won 3-0 in the Premier League encounter in October in one of the results which ultimately cost Villas-Boas his job.
And the Hammers completed a second successive win at White Hart Lane with a come-from-behind triumph to set up a League Cup semi-final with Manchester City.
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 last four.
Sam Allardyce hopes his Hammers, who had won just two of the 10 matches between visits to White Hart Lane, can gain a much-needed fillip from the triumph.
"It was a fantastic victory for us," Allardyce said following the match.
"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."