The Hammers beat Tottenham three times last season, adding a 2-1 Capital One Cup quarter-final win to a Premier League double that included a first win at White Hart Lane in 14 years.
They were memorable moments in a season to forget for West Ham, who flirted with relegation throughout, and provided something to celebrate for Allardyce, whose future at the club was questioned by their supporters.
"It was fantastic for us to beat our old rivals three times last year," he said. "But they are a top side and we'll have to hit the ground running. We'll have to hit top form from the first minute to the last.
"It's a very exciting fixture for the players, the fans and everybody else surrounding West Ham. It's a big local derby to start the season off and hopefully we can reproduce the performance that we did for the last game at home last year.
"Every game is important, whether it's the first or the last. If it goes as well as the last one did I'll be very, very happy on Saturday.
"It is a new season, they have a new manager. He'll assess the players he's got: he's brought some new players in, we've got some new players in, so it's a completely different scenario."
The 3-0 win at White Hart Lane was especially memorable as Allardyce named a side without a striker in it, and with Andy Carroll ruled out for four months and summer signing Enner Valencia not yet match fit, that option could again be in the manager’s mind for Saturday's meeting.
Mauro Zarate and Carlton Cole are in contention to lead the line and new recruit Diafra Sakho will also be hopeful of making his West Ham debut having arrived on Thursday.
"I'm looking forward to playing," said Sakho, who has signed from Metz. "It's more than a month now that I've been training for this and right now I think I'd be ready to pull on the club colours."