Egypt winger Mohamed Salah, the key figure in Liverpool's impressive campaign, was left out due to a minor groin injury as Jurgen Klopp tried to give his main man a chance to be fit for their decisive Champions League clash against Manchester City on Tuesday.
Danny Ings and Dominic Solanke looked rusty as they were given rare starts, with the latter failing to take either of two early chances. Roberto Firmino appeared as a late substitute in an attempt to find a winner, but third placed Liverpool had to settle for a point. They did, though, extend their unbeaten run in Merseyside derbies to 17 matches, as Seamus Coleman and Dominic Calvert-Lewin both failed to take late Everton chances.
Klopp had a big decision to make regarding his team selection, with Liverpool three days away from the second leg of their quarter-final against City following Wednesday's 3-0 victory The fact that he made five changes showed where his priorities lie at the moment.
Ings was starting a league match for the first time since Klopp took charge two-and-a-half years ago, having fought back from two cruciate knee ligament injuries, while Solanke was making only his fourth league start for the club. In addition, Nathaniel Clyne began a match for the first time in 11 months after recovering from a serious back problem, while central defender Ragnar Klavan was pressed into service at left-back, having played just 11 minutes since New Year's Day.
Inevitably, given those changes, Liverpool did not click as they usually do. Solanke lacked the kind of sharpness that Salah and Firmino have made second nature. Presented with two good chances in the first 16 minutes, he took neither. First he glanced wide from James Milner's angled delivery, and then, when Coleman made a mess of clearing Clyne's cross on the run, the striker could only steer his first-time shot straight at Jordan Pickford.
Pickford looks increasingly likely to be England's goalkeeper at the World Cup later this year, having grown in confidence as the season has gone on. His shot-stopping has rarely been in question, and he produced a fine flying save late in the half to turn away a shot from Milner, who had cut in from the left. Liverpool enjoyed the bulk of possession despite their disjointed look, which was partly down to Everton's lack of adventure.
Sam Allardyce had written in his programme notes about derbies being occasions to be inspired by, but his team lacked spark until the final 10 minutes and gave away the ball too often. Even though Everton did enjoy bursts of pressure, Cenk Tosun was a frustrated figure up front for the most part. Yet Liverpool goalkeeper Loris Karius still needed to be alert, making perhaps the save of the first half when he tipped away Yannick Bolasie's 25-yard curler, bound for the top corner.
The home side might even have won the match at the end, as the Turkey forward headed Theo Walcott's cross towards the far post, where Coleman just failed to turn the ball in. Calvert-Lewin then steered over with only Karius to beat. Liverpool were prepared to show aggression, with Ings involved in a confrontation with Coleman that needed the intervention of referee Michael Oliver and both captains to sort out.
It got the crowd going, but they would not have a goal to cheer.