Sherwood took over the London side for the first time since Andre Villas-Boas was sacked as manager after the 5-0 loss to Liverpool in the Premier League last Sunday.
Spurs grabbed the opening goal courtesy of Emmanuel Adebayor on 67 minutes only to concede twice in the last 20 minutes as a semi-final clash with Manchester City was wrestled from their grasp.
"I think, to be honest, they ran out of a bit of steam," he said. "I think they are fit enough to play a certain way, but I wanted to change the way we wanted to play.
"The problem we had was giving the ball away. There was a period after we scored when we were turning over possession and it's impossible to rest when you are out of possession. You need to rest on the ball and they need to recognise when is the right time to do that. I don't think they did that well enough, and that encouraged West Ham.
"I think they are fit enough but to play a certain way...when it's a complete change of mindset of how I asked them to play – I asked them to go a bit more gung-ho, and up and at them. You need to acclimatise to that."
Sherwood is unsure if he will be given the job on a permanent basis with Ajax coach Frank de Boer and Mauricio Pochettino of Southampton both linked with the vacant post.
Sherwood does not even know whether or not he will still be in charge of the side for Sunday's trip to Southampton.
"It's been different. It's madness, really," said Sherwood. "I'm not used to sleeping two hours at night.
"I'm waking up thinking about footballers. I said the other day, I slept like a baby – I woke up crying four times in the middle of the night.
"I'm up for a challenge, I always have been. I'm very opinionated. I know a certain way that I need to play. I think I can manage men, deal with them, be honest with them. The decision that's going on is out of my hands unfortunately. I've got to be in the frame, but it's not my decision."