Leeds almost went in front after the half hour when Danny Pugh's cross almost beat Liverpool keeper David Martin, but he managed to touch the ball onto the bar before James Smith played it to safety.
Adam Hammill drew the first save from Ian Bennett when he struck a powerful shot from 20-yards after a run by Jan Kromkamp.
But the first half finished with some controversy when, two minutes before the break, Calliste reacted to a challenge by Walton by headbutting the Leeds defender and Walton responded by grabbing Calliste, with both being sent off.
Leeds wasted two early opportunities after the break when Rothery picked up a loose ball inside the box but hit the ball high over the bar from just 12-yards, and then five minutes later Moore headed over when well placed.
Liverpool's Robbie Foy could have put them in front on the hour mark when he beat his marker three times before unleashing a left-foot shot which was pushed away by Bennett. Two minutes later Pugh struck a post with a fine 20-yard volley.
Ryan Flynn almost won it for Liverpool two minutes from time when he got on then end of a Smith cross, but his shot was again saved by Bennett.
Leeds: Bennett, Madden (Gray 75), Harding, Parker, Walton, Einarsson, Griffiths (Howson 60), Bakke, Moore, Rothery ( Bayly 81), Pugh.
Liverpool: Martin, Kromkamp, Smith, Antwi, O'Donnell, Hobbs, Hammill (Flynn 75), Peltier (Lindfield 83), Calliste, Guthrie, Foy.