The result hauled Klopp's team to within six points of leaders Chelsea heading into the holiday period.
The result hauled Klopp's team to within six points of leaders Chelsea heading into the holiday period, the perfect way for the club to prepare for their festivities.
"I'm really happy," said Klopp, who was experiencing his first trip to Goodison Park.
"We now have 37 points and that's good.
"It could have been 40-something but that's okay (they dropped five points recently against Bournemouth and West Ham after leading in both).
"We won't stop. Tomorrow (Tuesday) is our Christmas party and this is the first party we have had after a win!
"It's unbelievably close and difficult each week but it is still like this. You need to be ready for each game, play your best and collect the points.
"The play of Everton was wild football. They were chasing us in the first half. We could have done better but it is really difficult to adapt to something like that.
"I am sure in two or three months we can react much better but today it was a little bit of a surprise and we couldn't handle it."
Until Sadio Mane struck home a rebound from Daniel Sturridge's 94th-minute shot, the game's main talking point had been Ross Barkley escaping a red card after a high stamp, above the ankle of Liverpool and England midfielder Jordan Henderson.
"I thought it was a harsh challenge," said Klopp.
"You all saw it, I don't have to say anything about it. I think Ross is lucky and Hendo is lucky too that nothing else happened."
Klopp's Everton counterpart Ronald Koeman agreed Barkley could have been dismissed by referee Mike Dean.
However, as Liverpool defender Dejan Lovren was involved in a shoving match that followed the incident, the Dutchman believed the opposition player might have been dismissed having already been booked.
"It was a tough tackle, maybe it's a red," he said.
"But what happened after this is not a fair decision from the referee.
"Maybe it's a red for Barkley but, there was a reaction from several players but it was started by Lovren.
"He already had a yellow and the referee gave a yellow to (Seamus) Coleman and nobody else. If you're straight, you give Lovren his second yellow, Coleman a yellow and maybe a red card."
At least Barkley's England team-mate Henderson suffered no ill effects from the challenge and believes his friend was innocent of any ill intent.
"I think it was pretty late but I know Ross well and he's a good lad. I'm good friends with him," said Henderson.
"He mistimed the tackle and after the game he apologised.
"It was a little bit late but thankfully I'm alright and walking around. It was just mistimed and you're going to get them in derby games.
"It's a derby and it doesn't matter if you're friends off the pitch or on the national team.
"When you're on the pitch you give 100 percent to win the game and after the game you shake hands and move on. Ross is a good lad and I think he just mistimed one."
The game, and the manner of the goal, was a boost for England forward Sturridge who has been sidelined for over a month through injury and struggled for consistent fitness this season.
"You have Daniel and you're always thinking, when is the right time, is he ready for this?" said Klopp.
"Because it is not normal that after two training sessions a player can really help you but he helped us a lot tonight.
"In a very difficult game, he could make the difference."