Following their latest encounter at Goodison Park, this fixture has seen more goalless draws than any fixture in both English top-flight history (36) and Premier League history (12).
In an eventful encounter in the early kickoff, Liverpool hit the post three times while Everton goalkeeper Jordan Pickford produced a number of outstanding saves, including one in stoppage time from Mohamed Salah, to prevent Liverpool from scoring in the top flight for the first time this year.
The hosts also had a goal from Conor Coady chalked off by VAR for offside and hit the post in the first half through Tom Davies.
After witnessing his side fail to break down Frank Lampard's men, Klopp admitted were unlucky not to carry the day.
Klopp said after the game: "It was a real derby, super intense and with a lot of really spectacular moments."
"We hit the post three times, and a few unbelievable saves by Pickford. Wow. What can you do," Klopp added on BT Sport.
"You have to dig in really deep, that's what we did. In the end it's nil-nil, which sounds strange, but that's it."
"It's been a super intense week for us."
"On Wednesday night we had a really tough game and had to go to the wire, and a few days later you play here.
"I don't know how many derbies I've played now, quite a few, but it's always difficult and it was difficuilt today."
"This game was not bad, at all, it was just a tough one."
"I don't forget that they had a big chance. The goal was offside so I don't count that, but it was close, but when Ali made a save [from Maupay] that was proper. Apart from that we had bigger chances but it's okay now."
Liverpool have now picked up just two wins from their six games so far this season.
