The reigning Premier League champion slipped to a third successive home league defeat on Monday (AEDT), with the result leaving it well off the pace in the title race.
City now sits five points clear of nearest rival Manchester United but 10 ahead of Liverpool, while Pep Guardiola's squad also have a game in hand.
Mohamed Salah's penalty cancelled out Ilkay Gundogan's opener in an eventful second half at Anfield, but two blunders by Alisson helped City on its way to a record-equalling 14th successive win in all competitions.
"When you lose 4-1 it's not your day. Big parts of the game were brilliant from my side, we played really good football," Klopp said.
"In the first half we played really good football, against City it just means you are reading the game. Start of the second half, City changed the system slightly to a 4-4-2.
"It's a little adaptation and at the start of the second half we didn't give enough options to play and gave the first goal away. We just gave them a bit too much of an opportunity.
"We scored the equaliser and it looked like the game could now go in our direction. We made two massive mistakes, it's clear, everybody saw them, they used them, then 3-1 it's tough to take.
"The performance was good for a lot of time. Really good, high level, if we played more before like in these moments we would not be 10 points behind City.
"The goals - we made massive mistakes, if you make them against City it's the killer. That's why we lost the game."
Klopp felt the rest of the team did not help out Alisson for the stray passes that led to City's second and third goals, scored by Gundogan and Raheem Sterling respectively.
The Brazil international is the first Liverpool goalkeeper to make two errors leading directly to a goal in a single game since Loris Karius against Real Madrid in the Champions League final in May 2018.
"It's true as well that we didn't give him a lot of options, especially the first one," the Liverpool boss said.
"I think the second one there is no explanation, maybe he had cold feet or something, it sounds funny but it could be, but still the opportunity was there to kick it into the stands.
"But Ali has saved our lives many times and tonight he made two mistakes."
With a double-digit gap to City, Klopp confirmed his main focus is on sealing a top-four finish and a place in next season's Champions League.
They return to league action next Saturday, travelling to third-place Leicester City.
"It is of course our main target, that is clear, we will try everything," Klopp said. "We've enough games to play to secure that but we have to win games."