Kenny Dalglish's side were slow to get off the mark and quickly found themselves 2-0 down, with Lars Iver Strand sliding home for the hosts inside the first 10 minutes after a low cross inside the box from Havard Nielsen before Fegor Ogude slide home from the penalty spot.
Valerenga were perhaps fortunate to be given such a gilt-edged chance from 12 yards, however, as Yssouf Kone was clumsily tackled by Charlie Adam as he attempted to hit a first-time volley.
It was almost half-time before Liverpool got back into the match, as Andy Carroll rose highest to plant a trademark header beyond the despairing goalkeeper.