Liverpool began the second half in similar fashion as they played out the opening period by dominating much of the ball.
Kone-Doherty produced more good play by finding Lucas Pitt in the area, though stopper Waller was equal to his effort.
The winger then fired wide himself from a tight angle as the Reds stepped up their efforts in a bid to get themselves back into the game.
Joe Bradshaw then hit a driving shot from distance wide of the goal after an error at the back from Crewe allowed him to pick up the ball in the final third.
In the closing minutes, Kaide Gordon displayed clever feet inside the area as Liverpool pressed the hosts well, forcing them to give up the ball in their own box.
His placed effort, though, fell inches past the far post in what was the last of the meaningful action.
Liverpool: Mrozek, Ramsay, Williams (Nallo, 63), Lucky, Pitt, Laffey (Onanuga, 63), Spearing (Trueman, 46), Gordon, Kone-Doherty, Pilling, Sonnie-Lambie (Bradshaw, 62).
Unused subs: Misciur, Davidson, Pinnington.
Up next
Liverpool will next return to competitive action on Sunday October 26 with the visit of Everton to the Kirkby Academy in a 1pm GMT kick-off.
The Reds host the Blues in a Merseyside derby in Premier League 2, which will be available to watch live for supporters via All Red Video.
