Mata's brace would have grabbed the headlines on another day, but the Spaniard was overshadowed by Liverpool captain Gerrard, who was dismissed for a stamp on Ander Herrera within a minute of coming on at half-time in what will likely be his final appearance against United before leaving for LA Galaxy.
Former Chelsea man Mata opened the scoring in the 14th minute with a cool finish from a Herrera pass and then doubled the lead in the 59th minute with a sensational scissor-kick.
Daniel Sturridge pulled one back for Liverpool 10 minutes later before Wayne Rooney missed an injury-time penalty following Emre Can's foul on Daley Blind, as United moved five points clear of Liverpool in the race for fourth place.
Van Gaal told Sky Sports: "We played very well in the first half. Maybe as good as against Spurs [a 3-0 victory] but in second we didn't play very well.
"Like always, when you play against 10 you forget to press. We had unnecessary ball losses and we brought Liverpool into the game. Most of the players were thinking 'maybe [someone else] can do it'.
"We kept the ball and created a lot of possibilities, not big chances, but a lot of possibilities to score. I said whoever could beat the pressure shall win.
"Juan Mata was very good. He has always played good with me in my opinion. But sometimes you also need balance in your team and you have to select other players.
"Now he has played very well and did this position very well.
"It's an amazing result for the fans. We now have a gap from positions five, six and seven, which is very important."
