Two first-half goals from Inigo Baque at the Kirkby Academy saw the Spanish side take home the three points from the group-stage encounter.
Jack Bearne's 82nd-minute strike pulled one back for the young Reds and progression to the knockout stages of the competition can still be secured with a win at Wolverhampton Wanderers later this month in their final Group E fixture.
An early chance fell for Neil Critchley's charges before the visitors took control of the affair, with the newly-arrived Joe Hardy striking the side-netting inside two minutes after Leighton Clarkson's neat pass.
Liverpool goalkeeper Ben Winterbottom denied the Bilbao outfit on three separate occasions prior to the eventual opener.