The German coach looked on as Belgian striker Divock Origi came closest for the visitors at White Hart Lane, striking the crossbar with a close range header in the first half.
Spurs had chances too, primarily through Harry Kane and Clinton Njie, but both were denied by fine stops from Liverpool goalkeeper Simon Mignolet.
Despite a late long-range effort that slid past the Tottenham upright from Liverpool's Emre Can, the deadlock remained unbroken.
Klopp appeared happy with a point at a difficult away ground as well as the clean sheet.
He effusively embraced his players after marching on to the pitch at full time but later said his side could have earned the win had they been calmer and more confident in possession.
"The problem of the game was that when we had the ball we were not cool enough," Klopp told reporters.
"We didn't use our skills. We were a little bit too... hectic? Eager? We didn't see the right option."
Liverpool were without key players Saturday, including Christian Benteke, Danny Ings and Joe Gomez -- the latter two will be out for the rest of the season after suffering serious knee ligament injuries in the last week.
But the Anfield side still showed early signs of adopting the high pressing game and quick transitions that were such a prominent a feature of Klopp's last team, Borussia Dortmund.
"I'm satisfied with the start," said the Klopp, who succeeded the sacked Brendan Rodgers during the recent international break.
"We only had three days (of training) and Tottenham have a very, very strong and well-tuned team. It could be difficult, but I'm really satisfied.
"Now we have our own game, our own experience together, and we can go on working."
Klopp's hyperactive touchline antics and multitude of intense facial expressions have been as much the focus of attention as his coaching prowess since he became Liverpool boss.
And there was plenty to keep the cameramen snapping and TV cameras entertained Saturday.
The former Borussia Dortmund boss bounced up and down as he cajoled his team forward late on, kicking every ball from the technical area.
The result means Liverpool remains in 10th position in the Premier League table, one point behind Saturday's rivals Tottenham in eighth.
Liverpool is next in action Thursday when it faces Rubin Kazahn in the Europa League.