Injuries meant Klopp gave Divock Origi his first league start up front, and he hit the bar with a first-half header.
Tottenham’s best efforts saw substitute Clinton N’Jie and Harry Kane test Reds keeper Simon Mignolet.
Spurs are now unbeaten in their last eight Premier League games, since the opening day of the season
Liverpool started the game well and almost took the lead in the tenth minute. Emre Can got on the end of James Milner’s cross and his flick was met by Origi, but his header came back off the angle of post and bar.
The Belgian was unable to turn the rebound over the line from point-blank range and somehow Spurs survived.
It took almost half an hour for Tottenham to create their first real opening.
Adam Lallana’s stray pass fell to Kane and he pounced and fed N’Jie, who ran into the right-hand side of the area, but a superb reflex save by Mignolet saved Lallana’s blushes.
That chance sparked Spurs in to life, and they almost took the lead with 40 minutes gone.
Nathaniel Clyne’s tackle only diverted the ball into Kane’s path but his low shot was kept out by Mignolet’s legs.
Dele Alli was first to the rebound but Mamadou Sakho threw himself in the way of his shot and Klopp was able to breathe again.
And Spurs continued to dominate as Clinton N’Jie made the most of a mix-up between Martin Skrtel and Clyne, and he darted towards the edge of the area before smashing in a shot that fizzed just over the bar.
In the second half Liverpool got back into the game, however they had nothing to show for it as chances remained few and far between.
Spurs created a great chance with five minuets to go. Christian Eriksen teed up Kane on the edge of the area but Reds keeper Mignolet sprang to his left to push the ball away.
Just as the game seemed to be petering out, Liverpool almost won it when Can let fly with a snap-shot from the edge of the area that flew a fraction wide, however the game remained goalless to give Klopp his first point as Liverpool boss.