After losing heavily to Chelsea and Liverpool last week, Tottenham completed an unwelcome hat-trick with Dimitar Berbatov scoring with two early headers and substitutes Gilberto and Darren Bent wrapping up the scoring at White Hart Lane.
Curbishley woke up to reports suggesting his job may be insecure, although he feels his board are sympathetic about the problems he has had with players missing during his first full campaign at the club.
"I think they are realistic about it but we'll have to see on that score because it's a results business," the Hammers boss said.
"Up until this week we hadn't been too bad so we'll have to bounce back."
He added: "We're in football and nothing surprises anybody but I would have thought (they would understand). They are realistic about what has gone on. They get the update every Monday of the injury situation.
"Any other team that has had six or seven out every week would find it difficult. You can see the difference in teams with settled sides."
Spurs head coach Juande Ramos was pleased with his side's response after two defeats since winning the Carling Cup.
"The goals made it easier and we were in control for a large part of the match," said the Spaniard. "It was important to have a victory to recover people's esteem."