Mata scored a superb brace before Man United were awarded a penalty in the dying moments of the match when Emre Can brought down Daley Blind in the box.
Instead of giving Mata the chance to score his third goal, Rooney elected to take the penalty himself but his effort was saved by Simon Mignolet.
The 29-year-old was delighted with the three points but acknowledged that he should have given up the spot kick:
Very happy tonight. Fans were amazing. @juanmata8 great goals. Should of let him take penalty. And the United fan in the kop. Brilliant
The penalty miss was the culmination of a poor performance from Rooney, who has historically failed to produce at Anfield down the years.
Having scored five goals in six games prior to the match, fans may have expected Rooney to make more of an impact but he was subdued during the game. However, they will not be too disheartened thanks to a superb result coupled with a red card for Liverpool captain Steven Gerrard.