Matt Ritchie's second-half strike condemned Jose Mourinho's side to a second away defeat in a row in the top flight and left them 16 points behind leaders Manchester City.
Mata, who came off the bench in the second half as United chased the game, has now called on his team-mates to channel their "rage" into their FA Cup fifth-round clash with Huddersfield Town on Saturday.
"It's not easy to write after a defeat," he wrote in his blog. "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."
"We already have to focus on the FA Cup and Huddersfield. It will be a great opportunity to prove that a new win can help to forget [Sunday's] game."
6 - Jose Mourinho has now lost six times against Rafael Benitez in all competitions; only versus Pep Guardiola (9) has he suffered more defeats as a manager. Adversaries. pic.twitter.com/SBhGVfaH4c— OptaJoe (@OptaJoe) February 11, 2018
Mata also praised the club for its handling of the 60th anniversary of the Munich air disaster last Tuesday and paid tribute to former United midfielder Liam Miller, who passed away following a battle with cancer last week.
"The week has been very special for the club, in commemoration of the 60th anniversary of the air disaster in Munich that changed the history of Manchester United forever," he added.
"It was very emotional and it shows once again that this club is different. The Flowers of Manchester will always be remembered.
"Also, this weekend we got the sad news of Liam Miller's passing, another footballer who wore the United shirt. He was only 36. Here I'd like to send a hug to his family and friends on behalf of the whole team."