Following 3-0 defeats to both Hull and Galatasaray, the Reds at least got on the scoresheet and it was a much improved performance from Kenny Dalglish's side.
Dalglish named a full strength side featuring new signings Stewart Downing, Jordan Henderson and Charlie Adam and was rewarded by some sparkling attacking football.
But the defensive frailties remained and the visitors found themselves 2-0 down inside 20 minutes, Lars Strand scoring from close range on 14 and Fegor Ogude doubling their lead from the penalty spot (18) - with Glen Johnson culpable on both occasions.
Andy Carroll pulled a goal back after hooking home a Downing cross on 42 and from that point on, Liverpool dominated.
Charlie Adam was a whisker away from firing in a long-range equaliser just after the restart whilst Valeranga keeper Gudmund Taksdal Kongshavn pulled off a string of superb saves to keep his side ahead.
But Kongshavn was finally beaten on 83 as Daniel Agger crashed in a header and the Denmark defender looked to have become an unlikely matchwinner when he volleyed in from close range five minutes later.
However, Liverpool were denied victory in the dying seconds as Mohammed Fellah equalised with a shot that seemed to deceive a flat-footed Pepe Reina.