Dominic Solanke, starting down the middle with Roberto Firmino on the bench, was the main culprit as he wasted the two clearest chances of a drab encounter in front of England manager Gareth Southgate, while Loris Karius only had one Everton effort to deal with across the entire 90 minutes.
Everton were second-best for most parts, save a frantic final 10 minutes in which they put their illustrious neighbours under vast pressure but in the end a scoreless draw was inevitable.
"I think we controlled around 60, 70 minutes of the game, and then it got quite emotional, which is normal I expected that!"
The Toffees and Reds played out a lackluster 231st meeting amid wet conditions at Goodison Park with neither able to make the elusive breakthrough.
Everton stay ninth and are now nearly certain to miss out on a place in the top seven, meanwhile, as their winless streak against Liverpool - stretching back to October 2010 - was extended by a further match.
"It's not our first-choice result", Klopp admitted.
Everton defenders Leighton Baines, Michael Keane and Phil Jagielka will be pleased to have kept a clean sheet in front of the worldwide coach, albeit against weakened opposition and not completely assured in their work. I liked it. We were intense but not too aggressive.
"It's a nice place to come".More news: Manchester City 2 United 3
Man, do we love that "best day in my life" quote from Klopp, who can be absolutely hilarious at times.
Yet Liverpool goalkeeper Loris Karius still needed to be alert, making perhaps the save of the first half when he tipped away Yannick Bolasie's 25-metre curler, bound for the top corner.
He continued: "It was a nice one!"
"I don't feel like I'm on trial", he said.
Presented with two good chances in the first 16 minutes, he took neither. This was the first Merseyside derby since 1992 to end without a card of any description. But it's a game of football - all I do is try my best and if I keep a clean sheet I am happy.
Klopp said: "A point is OK". The job was to work hard and enjoy the game, really, and then get a result and they were like this. He needs more time and he will deliver goals. And Clyne is such a model player.
Liverpool were without keyman Mohamed Salah in the clash and it was visibly noticed as they lack the necessary bite going forward.
Roberto Firmino and Alex Oxlade-Chamberlain both appeared as late substitutes in an attempt to find a victor, but third-placed Liverpool had to settle for a point. "It was a good performance, not brilliant, but probably the most mature since I came here".