The Black Cats are desperate for points and came close to earning one against the high-flying Reds on Saturday afternoon, before two goals in the last 15 minutes wrapped up the win for the home side.
Having climbed off the bottom last week Sunderland returned to the foot of the Premier League having had just 22 per cent possession and managed only one shot on target.
"It wasn't for the purist; but it's not our job to entertain the Anfield crowd. Our job was to come and try and get a result," said Moyes, whose failure to win at his bogey ground extended to 14 matches.
"I think the Sunderland fans could see how hard the players were trying out there and how much effort they were putting in and they stuck with the game.
"We were close, but not close enough."