With five games left for both Liverpool and City, the title race looks destined to go down to the wire.
Liverpool, trying to become the first English club to win all four major trophies in one season, now turn their attention to Wednesday's Champions League semi-final first leg against Villarreal.
"A football game has two halves; thank god. In the first half, we didn't pass quick enough. At half-time, I told the players it was easy to improve. We had to work hard for it, but all good," Klopp said.
"There are not a lot of points we can drop, the next one is always waiting around the corner. That is the situation we are in."
Everton have lost eight successive away games for the first time since 1948 and are in grave danger of relegation to the Championship.
Frank Lampard's men were dumped into the relegation zone by Burnley's 1-0 win against Wolves earlier in the day.
They sit two points behind Burnley with a game in hand as they try to avoid playing in the second tier for the first time since 1954.
"The gameplan was understanding they are one of the best teams in the world. We wanted to be disciplined. If we get the first goal, the game feels different," Lampard said.
"We have to take that spirit forward to the final games. We'll give everything until the end."
In the 62nd minute, Origi combined with Mohamed Salah, who crossed to the far post for Robertson to head his second goal this season.
Origi, a regular scorer against Everton, grabbed the second goal with a close-range header in the 85th minute as Liverpool made it 12 wins from their last 13 league matches.