United hit 20 shots in their encounter against a Bournemouth team who played with 10 men for the entire second half, but were held to a draw as Joshua King's penalty cancelled out Marcos Rojo's earlier strike.
The game grew tense towards the end of the opening period when Zlatan Ibrahimovic and Tyrone Mings clashed several times. The Bournemouth defender stamped on Ibrahimovic's head and the Swede retaliated a few moments later with an elbow to the face, having previously thrown Mings to the ground in a separate tussle off the ball.
Though both players went unpunished, Andrew Surman was shown a second yellow card before the break for pushing Ibrahimovic.
Mata admitted it was a stiff game, but believes United can release any lingering anger when they take on Russian side Rostov in the away leg of their last-16 tie.
"All of us felt very frustrated," he wrote on his official website. "Unfortunately, we have that sense of deja vu again. We played good football, we created chances, but yet again we weren’t efficient enough to turn that into a better score.
"As I always say, the good thing is that soon after a defeat you have an opportunity to make it up. Football doesn’t stop and it always gives you another chance to release your rage doing what you like most.
"We have four games to play before the international break and each of them is going to be a special challenge. First of all we have the Europa League tie against Rostov, including a long trip, that is going to test the strength of the team in every sense. The Russian side is particularly strong at home: this season they have defeated Bayern Munich and Ajax, for instance. That gives you an idea of how tough they are.
"And four days later we will play in the FA Cup against Chelsea at Stamford Bridge. Another key game, a top-level tie in such a special competition. We will need to play a great game if we want to celebrate back-to-back FA Cup titles at Wembley."
Mata's Spain team-mate Fernando Torres was suffered a head injury and was knocked unconscious during Atletico Madrid's game against Deportivo La Coruna in Thursday, leading to him being monitored in hospital overnight.
But the striker returned to the Vicente Calderon on Sunday, watching his side beat Valencia 3-1 from the stands, and Mata was delighted to see he was okay.
"The most important moment of the weekend, in my opinion, did not happen on the pitch," he added. "It was a relief to see Fernando Torres seated in the box at the Vicente Calderon, already recovered after the big scare a few days earlier, and the affection to him showed by the crowd.
"I’m very happy that it wasn’t anything serious; he will be back scoring goals very soon, as always."