Craig Lindfield scored Liverpool's goal but there were injury worries for the Reds as Jimmy Ryan and captain Jay Spearing were forced off after picking up knocks.
The injuries are worrying for Liverpool as the first leg of the FA Youth Cup semi-final with Newcastle takes place next Saturday and both Spearing and Ryan are key players for Steve Heighway's side.
"It's not the ideal preparation for the semi-final but we are hoping Jay and Jimmy will recover in time as they are key players' for us," Academy coach John Owens told the club's official website.
"It was a typical derby in the sense that it was a battle at times and very competitive. Craig gave us the lead when he met Ryan Flynn's shot across the face of the goal but we couldn't hold on. Everton played well in the second half and got an equaliser which they probably deserved."