The first half was a cagey affair with chances at a premium for both sides. Everton offered very little going forward, while Mohamed Salah was twice denied by goalkeeper Jordan Pickford.
Everton improved after the break and saw more of the ball but rarely tested Alisson in the Liverpool goal.
Meanwhile, Salah was guilty of wasting another opportunity as the Reds picked up a third successive draw away from home in the Premier League.
Salah's Lack of Ruthlessness Should Worry Klopp
Jurgen Klopp kept faith with Divock Origi, Sadio Mane and Salah in attack, and it was the Egyptian who had the best chances to score at Goodison Park.
Fabinho slid Salah in just before the half-hour mark but Pickford stuck out a strong right hand to save his effort.
Football writer Leanne Prescott felt Salah could have done better:
Another chance followed for Salah on 58 minutes after a strong run forwards by Joel Matip. However, he took a poor initial touch which allowed Seamus Coleman and Pickford to smother the danger.
Miguel Delaney at the Independent said Salah is lacking sharpness:
The Egyptian's lack of ruthlessness in front of goal should concern Klopp as the Reds reach the business end of the season.
Salah has now gone four games without a goal and has managed just four in 11 appearances for the Reds in all competitions since 2019.
He has also been guilty of missing plenty of chances in front of goal:
Liverpool have drawn four of their last six league matches, which has seen them lose their lead at the top of the table and slip a point behind Manchester City.
The Reds have just nine games left to play in the league and badly need Salah to rediscover his goalscoring touch quickly if they are to go on and pip Pep Guardiola's side to the title.
Everton Going Nowhere With Underperforming Silva
Everton will be pleased to take a point off the Reds, but the draw means they are still without a victory against their local rivals since 2010.
The hosts very rarely looked like scoring either, particularly in a first half when they struggled to keep the ball and would have been relieved to hear the half-time whistle.
Manager Marco Silva's tactics came in for criticism during the game:
The Toffees played with greater intensity after the break, but the closest they came to a goal was a header by Dominic Calvert-Lewin that was saved by Alisson early in the second half.
WhoScored.com highlighted the pressure Everton were under:
Everton also needed Michael Keane to put in a superb display in central defence to deny the Reds:
Silva did show some attacking intent with his changes in the second half. He brought on Richarlison, Cenk Tosun and Andre Gomes, but it was Liverpool who looked the more likely side to score in a tense finish.
Silva's direct tactics were simply ineffective against a Liverpool side with the commanding Virgil van Dijk in central defence. The hosts were fortunate to catch Salah on an off-day, but a change of approach is needed if Everton are to progress beyond mid-table obscurity.