I think there were two factors that stopped Liverpool recording a more convincing win. One was external, the other internal.
We tend to assume that in English football, referees aim to be fair and don't exhibit bias to one side or the other. I found Kevin Friend's display quite disturbing as he was clearly trying to help Sunderland. All through the game he was denying Liverpool free kicks for blatant fouls by Sunderland players, but when he had the opportunity he gave Sunderland free kicks for trifling offences.
The second factor was the club's own fault for the mindless pre-match watering of the pitch which always works against us rather than the opposition. In the first half, our forwards were constantly slipping. Even when they didn't actually fall over, their ball control was suffering because of the slippery surface.