The hosts had the most obvious opportunity to score late in the game, after Alisson Becker spared Dominic Calvert-Lewin’s effort.
Tom Davies at that point hit the post from the bounce back.
The outcome implies Klopp’s men will presently win the title against Crystal Palace on Wednesday, gave Manchester City neglect to beat Burnley on Monday.
“I liked our defending and high midfield press but we didn’t have enough chances for the possession we had. We were dominant but they had the biggest chance and that’s how it is.
“We were lucky in that moment. In the end, Everton defended really well and we were not smart enough to use the space we had,” Klopp told Sky Sports.