Jurgen Klopp’s side picked up following the top-flight resumption on Wednesday needing two wins to secure their first English title for 30 years.
But Liverpool looked rusty in their first game in 106 days following the coronavirus lockdown.
Despite their underwhelming display at Goodison Park, Liverpool are now 23 points ahead of second-placed Manchester City.
If City drop points at home to Burnley on Monday, then Liverpool can clinch the title against Crystal Palace at Anfield on Wednesday.
A City victory would delay Liverpool’s coronation until at least their clash with Pep Guardiola’s team at the Etihad Stadium on July 2.
Liverpool have won just two of their last seven games in all competitions.
Reds star Mohamed Salah was left on the bench due to fitness concerns, while Andrew Robertson was also sidelined and they were not at their best as a result.
Liverpool improved after the break and Naby Keita fired just wide before Virgil van Dijk’s header was saved by Jordan Pickford.
But it was Everton who came closest to a winner on the break when Dominic Calvert-Lewin’s effort was saved by Alisson Becker and Tom Davies fired the rebound against the post.