The Reds were in complete control but failed to properly kill off the game, never building on Mohamed Salah’s sensational opener just before half-time.
That resulted in a penalty which Wayne Rooney put away emphatically for his first goal in a Merseyside derby.
We look at five things we learned from the match at Anfield.
Klopp gets it wrong
When the teams were announced, the talk before the game was all about the five changes for Liverpool that Klopp had made.
The Reds have now made 59 changes to a starting XI in the Premier League this season, the most any side in England’s top division by a long way – West Ham United follow them with 39.
There was a lack of creativity without Coutinho in the middle of the pitch, with the full-backs and wingers looking like the best chance to create something, and perhaps that was Klopp’s plan, with Cuco Martina struggling and Jonjoe Kenny inexperienced.
It looked like it was the perfect decision too, with Firmino and Coutinho getting a rest ahead of a busy December, and even there was time for Salah to come off too at 1-0.
But the problem was, despite their dominance, they were only one goal up and never killed Everton off.
The Reds managed just three shots on target, meaning they had 20 shots off target, and that just isn’t good enough.
Liverpool looked weaker without Salah on the pitch, and failing to take the chances means Klopp’s changes look like a massive mistake now – if they had their A team on, they would surely have picked up all three points.
A win would have seen them draw level with Chelsea on points, but instead, they blew the opportunity, and that has to be on Klopp as their Merseyside rivals were definitely there for the taking.
Liverpool need better than Lovren
Speaking before the game, Lovren said: “I’m feeling in the best shape I’ve ever been here at Liverpool and hopefully in the next four or five years I can stay here and show my best here at the club, enjoying every game.”
Liverpool fans will be hoping he doesn’t stay at Anfield for that long based on today.
The 28-year-old Croatian has come in for criticism from a number of Liverpool supporters this season and based on the Merseyside derby it’s easy to see why.
Everton had created absolutely nothing and Calvert-Lewin was going nowhere.
Despite that, as the ball fell to the young English forward in the box with 15 minutes left, the former Southampton man decided the best thing to do would be to clearly push him in the back.
As soon as he decided to put his hands on the forward’s back, he made the penalty decision easy for Craig Pawson, even if Calvert-Lewin made the most of it.
It was pure stupidity and underlined why Liverpool will never mount a true title challenge with him as first-choice centre-back.
Klopp needs to replace him in the backline. Returning with a bid for Virgil van Dijk in January looks more likely and more crucial with each poor performance.
Allardyce needs January reinforcements
Despite Everton’s big spending in the summer, the squad simply isn’t good enough.
They were hanging on for large parts of the game despite the scoreline and barely got out of their own half for the majority of the 90 minutes
While Calvert-Lewin won more aerial duels than anyone else on the pitch (five), which is no surprise – no-one’s won more than him in the league this season – they were toothless up front from open play.
They had only a handful of touches in Liverpool’s box and when Calvert-Lewin won the ball up front, there was no-one with him to get it to.
Gylfi Sigurdsson wasn’t particularly noticeable, while the weakness at full-back in particular was underlined, with Martina at left-back particularly struggling and not being strong enough on multiple occasions.
Of course Salah is a tough player to play against, but the Toffees will surely need better cover for Leighton Baines.
They’ll want players who seem to fight more for the team and who can provide a real threat up front. Managing three shots, including one penalty, simply isn’t good enough.
Yes, they got a draw today, but that was down to opposition error rather than anything else. That can’t be relied on in the future.
Jordan Pickford’s passing can disappoint
There’s no doubt that there’s a lot of hype for Jordan Pickford, with Everton being praised for bringing in the former Sunderland keeper last season, despite him being part of a leaky Black Cats back line.
His passing has been hailed as one of his best assets, with fans across the country in shock as he picked out an incredible 75-yard sideways volleyed pass to pick out Calvert-Lewin against Hajduk Split in an August Europa League tie.
In fact, former boss David Moyes hailed his passing to that of an outfield player last season.
“He’s obviously a very big kicker, I thought some of his passes against Watford recently, it was like watching a top midfield player,” said the then Sunderland manager.
“He’s just got to be careful, that it isn’t something he needs to do to get noticed or to be seen, because then it adds risks to his game. At the moment he’s not doing that, he’s limiting it.
“He’s a very good passer, he can go short, he can play long, it is such a big part of goalkeeping these days.“
While that may be an asset at times, he needs to be consistent more often. In the first half in particular, his distribution was awful at Anfield, with an accuracy of just 36 per cent. That slightly improved in the second half, giving him 42 per cent overall, but that’s still not ideal.
He needs to do better or he’s only putting his team under pressure straight away.
Salah: The best in the Premier League?
Chelsea fans must have been feeling blue when they saw Liverpool’s line up with former Blues Salah and Solanke starting in the Reds’ front three.
The Egyptian has been arguably the best Premier League signing of the summer and he just can’t stop scoring.
His goal just before half-time broke the deadlock, with the Egyptian overpowering Martina, going past Idrissa Gueye and firing an unstoppable shot with his left foot into the top right corner of Pickford’s goal.
Could have been two just after the break, got on the end of Milner’s cross, jumped above Kenny but headed wide.
He completed more dribbles (seven) than any other player on the pitch, had more shots (seven) too. He’s simply Liverpool’s biggest threat.
When he went off after 67 minutes, Martina will have been the most relieved man in Anfield after the torrid afternoon he had at the Egyptian’s hands.
It’s no coincidence that the Reds looked a lot more toothless without the Egyptian on the pitch, surrendering their lead.