Spurs are yet to win at their new temporary home this season after Burnley snatched a 1-1 draw courtesy of Chris Wood's stoppage-time equaliser.
They are now 14/1 with Sky Bet to win the Premier League title, behind Manchester City (11/8), Manchester United (2/1), Chelsea (5/1) and Liverpool who are 11/1.
A week earlier Spurs lost 2-1 at home to Chelsea, and their sorry record at the national stadium now reads just one win from their last 11 matches.
However, defender Alderweireld insisted their surroundings are not an issue.
"I don't agree, because if we score and it's 2-0 or 3-0, then it's a good game from us," he said.
"It was like Chelsea, we played a good game as well, so I don't buy that.
"It was not an easy game. Burnley are strong, they defend all the time, they counter-attack, use set-pieces as well, every ball comes into the box.
"But in these games we have to finish it, we have to be clever.
"They defend with 10 men behind the ball so it's difficult to create chances. You have to be clinical in your passing, in playing forward and then if you get three or four chances you have to finish the game a lot earlier."
Wood marked his Premier League debut for Burnley with a memorable goal.
The Clarets' record signing ran on to Robbie Brady's pass before slotting the ball past Spurs keeper Hugo Lloris to cancel out Dele Alli's strike in sensational style.
"Everybody looks at you as a striker when you come into a club to get off the mark and get up and running and it's nice to have done that," Wood told the club website.
"Thankfully it hasn't taken a long time but it's extra special because we got a good point away from home and a point the lads deserved after the fighting spirit we showed."
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