The Hammers, promoted as Championship play-off winners, have surpassed all expectations so far this season and currently sit in joint sixth position in the Premier League after 12 matches.
The Londoners last week earned a creditable win at Newcastle, but they now embark on a difficult run of fixtures that includes games at Spurs, Manchester United, Chelsea and Liverpool.
West Ham have not won at White Hart Lane since Ian Wright and Marc Keller guided them to victory in 1999, but Allardyce thinks his team are shaping up well ahead of the short trip across London.
He told the club website: "We go to Tottenham full of confidence and hope to get some of the injured players back. We'll need to be as good if not even better than we were in our away wins at Queens Park Rangers and Newcastle as an attacking force.
"We've got to rely on our superb defensive qualities and then we've got to try to work on the areas that Tottenham leave exposed, particularly when we get got hold of the ball. If we can marry those two together then hopefully we can give a performance similar to our recent ones and try to get a result.
"We'll have to be on top of our game, as we had to be against Stoke. We played our top game in the second half and deserved to beat them but couldn't quite do it."
Right-back Joey O'Brien was the unlikely goalscorer in the 1-1 draw with Stoke and the 26-year-old is also feeling positive ahead of the game at Spurs.
He added: "I picked up the ball and tried to play a one-two with Momo Diame but it did not come back to me, as it went wide to Gaz O'Neil instead. He has a lot of quality on the ball and his delivery is very good so I continued my run and took a chance.
"He smashed it across goal and I was in the right place at the right time and the ball was just where I wanted it.
"We will go (to Tottenham) to get at least a point, but we know it is going to be a very tough game because they are a top team. We have shown in recent weeks how well we can defend against Manchester City and Newcastle United. Nobody expected those results so we know, if we play well, we can take something from the game."