Laura Coombs had fired the Reds into the lead but the Blues equalised following a set-piece.
Scott Rogers’s side dominated the game for long spells but their failure to take their chances cost them the extra two points in the Women’s Super League.
Following their midweek defeat at Arsenal, Liverpool Ladies started brightly as they took the game to the Blues in front of an excellent crowd of 1,146 at Tranmere Rovers.
Caroline Weir fired an early effort narrowly wide from distance following a superb pass from Sophie Ingle, and when the Scotland international tried her luck again with that trademark left-foot, Everton stopper Kirstie Levell made an excellent stop.
Left-back Alex Greenwood was enjoying an excellent afternoon in a more attacking role on the wing and she was a constant threat to the Everton defence. One superb cross almost led to the opening goal but Coombs was denied by an excellent block from Gabby George.
Rogers’ side then had the woodwork deny them twice. Firstly on 39 minutes a superb reverse pass from Weir gave Bethany England a sight of goal but her effort struck the bar.
Gemma Bonner was then unlucky a few minutes later when she saw her header also strike the bar following a corner.
Three minutes after the restart the breakthrough arrived for the Reds. Some excellent play down the left saw the ball fall kindly to the feet of Coombs and the No.8 made no mistake as she found the net.
Weir then came so close to what could have been a WSL goal of the season contender. Collecting the ball on the left side of the penalty area, the No.10 turned sweetly before seeing her audacious chip just clear the bar and land on the roof of the net.
On 59 minutes the Reds thought they had doubled their advantage when a Greenwood free-kick from the right curled straight into the back of the net, but the celebrations were cut short after the referee indicated an alleged push in the penalty area.
Everton claimed their equaliser on 65 minutes when substitute Jodie Brett netted from close range following a corner
The Blues then missed a glorious chance when a cross from the left found Chloe Kelly unmarked but the striker could only miscue her effort wide. It was a big let-off for the Reds.
Liverpool Ladies then created some fantastic opportunities but try as they might, they just couldn’t find the winner.
Niamh Charles, making a welcome return to action from the bench, hit the post, and Ali Johnson and England both had great chances but failed to make a telling contact.
Liverpool Ladies: Chamberlain, Murray, Harris (Johnson, 83), Greenwood, Bonner, Ingle, Longhurst, Coombs, England, Weir, Hodson (Charles, 57).