By FOX Sports staff
The result does little good for either side in their bid to finish in the European qualifying spots in the Barclays Premier League, but both only have themselves to blame after combining to produce a lacklustre encounter.
Here, FOX Sports rates the players that took to the field at Anfield on Sunday.
Pepe Reina - 7
The Spaniard had a couple of nervy moment but did well overall and showed clean hands whenever he was called into action.
Glen Johnson - 6.5
Although normally known more for his attacking prowess, Johnson did well at the back to contain the usually-dangerous Steven Pienaar and rarely let the South African out of his sight.
However, he probably could have done more in pushing forward considering his side were really lacking in energy.
Jamie Carragher - 7.5
In his 30th and final appearance in the Merseyside derby, Carragher was his usual steady self in the heart of the Reds defence and was always strong in the challenge.
Daniel Agger - 6
In the last few seasons, Agger has firmly established himself as Liverpool's premier centre-back but Sunday's game was one of the few times he has really been exposed as he struggled to contain Marouane Fellaini.
The Belgian's physical and aerial strength was too much for the Dane to handle and he was always second best in one-on-one battles.
Jose Enrique - 7
After a short spell where he was relegated to the bench, the ex-Newcastle man has come back strongly and has now reclaimed his status as Brendan Rodgers' first-choice left-back.
The Spaniard stuck to his direct opponent like glue all afternoon long but also pushed forward to good effect, whipping in a couple of useful crosses into the box.
Lucas Leiva - 6.5
Lucas manfully stuck to his task of protecting the Liverpool backline but perhaps could have done more when he had the ball, given he was the one midfielder Everton did not really press in possession.
Steven Gerrard - 8
As always, Gerrard showed he is the man for the big occasion as he put in another impressive display in a crunch clash.
Unfortunately for him, too few of his team-mates could match his performance but the Reds skipper still almost singlehandedly inspired his side to victory.
Stewart Downing (off 79') - 7
Downing is slowly finding the form that convinced the ex-Liverpool boss Kenny Dalglish to splash a reported £20million for his services.
At times, his delivery from the wings is still erratic but he is starting to cause opposition full-backs more problems than he used to.
Jordan Henderson (off 66') - 6.5
Like Downing, Henderson also had to endure a difficult start to life at Anfield but he has shown promising signs in recent weeks.
Unfortunately, he really struggled with the pace of Sunday's derby and it was no surprise to see him hauled off shortly after the hour mark.
Coutinho - 7.5
Luis Suarez's lengthy ban may have robbed the Reds of their focal point in attack, but in Coutinho, at least the Anfield faithful still have someone to dazzle them.
The former Inter Milan man was never afraid to sell his opponent a trick or two and, along with Gerrard, looked the most likeliest source of a Liverpool goal.
Daniel Sturridge - 7
While it wasn't one of his best games in recent times, Sturridge deserves some credit as he continues to show he could just be the long-term strike partner to Suarez.
The 23-year-old has an uncanny knack of finding space in the attacking third and is never afraid to shoot, although he does need to learn when it might be better to pass the ball on.
Fabio Borini (on 66') - 5
Borini was brought on for Henderson in the 66th minute but struggled to get a sniff of the ball.
He must be one of those sweating over their future at the club after a less-than-impressive year with the Reds, although it must be said he hasn't had the best luck with injuries.
Martin Skrtel (on 79') - N/A
Skrtel was thrown on 11 minutes from time to give Liverpool more height but had little time to make a real impact.
Tim Howard - 7.5
Although he had a relatively fuss-free outing, Howard was called into action on a number of occasions but was always equal to the task.
His most notable save came early on in the second half when he stood tall to deny Sturridge in a one-on-one situation.
Seamus Coleman - 5.5
Coleman was one of the few Everton players who failed to do their bit on Sunday as he was anonymous throughout the 90 minutes.
Sylvain Distin - 7.5
Although he seems to actively avoid the spotlight, there is no denying Distin has been one of the Premier League's best defenders over the past decade.
Despite now being 35, the Frenchman remains capable of keeping pace with most of his younger opponents and provided a brilliant block to keep out Gerrard's goal-bound shot in the second half.
Phil Jagielka - 8
Likewise, Jagielka has established himself as one of the competition's best defenders and he produced another fine display befitting of his status as an England international.
The former Sheffield United man read the play brilliantly and regularly weighed in with timely interceptions, but was also brave and denied Coutinho with a perfectly-timed tackle towards the end of the opening 45.
Leighton Baines - 7.5
Baines was at his barnstorming best on Sunday and was effective both in defence and attack.
Kevin Mirallas (off 75') - 5
Despite having produced some brilliant displays throughout the season, Mirallas was a peripheral figure throughout Sunday's derby and really struggled to come to terms with the magnitude of the contest.
Darron Gibson - 7
While Gibson is yet to really find consistency to his game, he has displayed on several occasions why he was so close to breaking through at Manchester United.
Blessed with a good range of passing, Gibson is capable of dictating the tempo for the Toffees and did well against Liverpool's more-illustrious midfielders.
Leon Osman - 6.5
Osman has been one of Everton's most-loyal servants over the last few years and while he offered his usual tireless running on Sunday, he wasn't the tidiest with his distribution.
Steven Pienaar - 6.5
Pienaar never stopped trying in Sunday's derby but his threat was well nullified by Johnson.
Marouane Fellaini - 7.5
At times, it looked as though Fellaini was having fun bullying Agger into submission with his sheer strength.
It was almost impossible to win possession of the Belgium international, although he needs to stop flailing his arms around when contesting in the air as it could very easily have seen him get into trouble with the referee.
Victor Anichebe - 7
Anichebe did not exactly have the best supply but to his credit, he worked hard all evening long and did well to hold up the ball in attack.
Nikica Jelavic (on 75') - N/A
The Croat, who was struggled for form this season, could have been the hero after coming on in the 75th minute but failed to make any sort of impact.