Manchester United boss David Moyes lamented the concession of the second penalty, just moments after the second half began, as the key moment in his team's demise.
Phil Jones barged into Joe Allen and prompted referee Mark Clattenburg to point to the spot.
"It was a game littered with penalty kicks and decisions - some were right and some were wrong. It was a tough day for us," he said.
"At half-time we were 1-0 down to a penalty kick, I didn't think there was much in it. To give away one 20 seconds or so into the second half it made it a real upward climb for us after that."
When asked if Liverpool were the better side, though, Moyes was blunt, saying: "Yep."