The Reds have now won just two points from a possible nine so far this season, and have scored only one goal, and that was a twice-taken penalty by Michael Owen against Chelsea.
Czech international Vladimir Smicer, who was making a welcome return from injury, had the first shot on target in the first minute.
In the 19th minute a 20-yarder from Spurs new boy Helder Postiga slid past the post thanks to the intervention of Reds keeper Jerzy Dudek.
Four minutes later Gerard Houllier's side were back in control as El Hadji Diouf, followed by new signing Harry Kewell, took the ball to the other end of the pitch.
However, Smicer eventually sent the Australian international's pass sailing over the crossbar.
Finnish defender Sami Hyypia had an effort disallowed for a foul when he headed Diouf's corner into the back of the net in the 54th minute.
The crowd roared in the 73rd minute as Liverpool and England midfielder Steven Gerrard looked as though he had broken the deadlock.
But his shot flew past the post without any help from Spurs keeper Kasey Keller.
The Reds continued to dominate and Milan Baros went close with an overhead kick in the 79th minute before Keller had to be alert to deny Gerrard.
With just five minutes left Baros missed an open goal while Danny Murphy went close with a last-gasp free-kick.