Other results over the weekend restricted United's strength in second place, and now the club only have a two-point cushion in the Premier League table.
In his weekly blog, Mata wrote: "It's not easy to write after a defeat. The truth is, after losing an away game you think a lot about it on your way back home.
"You remember every play, every moment, and you try to change the outcome but obviously that's impossible. You can't turn back time, so the only way to carry on is to turn all this rage into a desire to win, work and attitude for the next game.
"The 1-0 in Newcastle hurts because we had chances to score both in the first and in the second half, but they took better advantage of their weapons."
The Red Devils will switch their attention to the FA Cup this weekend when they take on Huddersfield Town.