After an encouraging start by the visitors, Divock Origi headed against the crossbar from close range.
Spurs weathered an early storm and would have been disappointed not to go into half time ahead after Simon Mignolet denied Clinton N’Jie and Harry Kane brilliantly.
The second half was a more stale affair, with Mignolet called into action to repel Kane again late on as neither side could force a breakthrough.
In Klopp’s first taste of Premier League football, his Liverpool team set about trying to emulate the high energy ‘gegenpressing’ so synonymous with the German’s highly successful Borussia Dortmund team.
The Reds showed promising glimpses in the early stages and were within the width of the woodwork of the opener when Origi flicked Emre Can’s header onto the woodwork with Hugo Lloris beaten.
But that insatiable early intensity understandably faded after 20 minutes as Spurs grew into the game, and Liverpool relied on a stunning save from Mignolet to deny substitute N’Jie to remain level.
The Belgian shot-stopper then did well to save Harry Kane’s fierce drive before Mamadou Sakho made a goal-saving block to repel Dele Alli’s volley from the rebound.
N’Jie launched a fizzing shot just over Mignolet’s crossbar soon after as Spurs finished the half strongly, but were unable to find a breakthrough against a resolute visitors’ defence.
After the break, goalmouth action was at a premium with Kyle Walker testing Mignolet from distance, while Adam Lallana had tentative appeals for a penalty waved away.
Origi, starting because Daniel Sturridge had suffered a knee problem, then engineered some space but shot straight at Lloris before Mignolet turned away another stinging Kane drive.
Can flashed a low shot just wide as the game drew to a close, but Spurs were not to be broken down as Mauricio Pochettino’s side extended their unbeaten league run to eight games.