In a game of few chances, the Blues had the best with Tom Davies hitting the post at the end of Alisson Becker had saved well from Dominic Calvert-Lewin.
Out of the impasse, which has gone from Liverpool closer to their goal of winning the title for the first time in 30 years, was the first of nine games in 36 days for europe and world champions.
Jurgen Klopp will now review its options after having rotated his squad significantly to Goodison.
And here, we look ahead to the changes the Reds boss could do when his side into action at home to Crystal Palace on Wednesday.
Only two of the five who started in Liverpool’s last match three months ago have been in the XI against Everton.
There will be a continuation of the rotation, with James Milner with a hamstring problem and concerns over Joel Matip’s toe injury.
At least Klopp has two great options, with Andy Robertson ready to come in at left-back to replace Milner and Joe Gomez, who came on his team-mate before half-time at Goodison, primed to replace Matip at centre-back.
Trent Alexander Arnold, Virgil van Dijk and Alisson Becker will continue in defence.
The question Keita
Naby Keita was one of the few Liverpool players to show anything like their best form this Sunday.
However, this is only his fifth Premier League start of the season and, after having been hampered by injuries this campaign, Klopp will surely be tread with caution, because the schedule ramps up after the trip to Manchester City, on the Thursday of the week.
Gini Wijnaldum, a second half substitute, the urge to action, while Alex Oxlade-Chamberlain, who played for 45 minutes at Everton, could work in a more central role.
Fabinho finished strongly on the weekend and needs minutes to build his sharpness, and Jordan Henderson appears to be another likely starter.
In spite of Liverpool being allowed to five substitutions, Mohamed Salah remained in the sides of Adrian, Harvey Elliott and Neco Williams sat in the stands throughout the weekend.
Salah had missed the friendly match against Blackburn Rovers earlier this month and was also absent from a number of training sessions.
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However, as with Robertson, Klopp is now at hand of the Egyptian a start, with Takumi Minamino likely to drop to the bench.
Divock Original has not fired in his second half cameo, Xherdan Shaqiri is injured while Oxlade-Chamberlain is another option on the right.
It may be too early to Elliott or the one of Liverpool, other young people, starting with the title, which has not yet been set.