The Spaniard gave United the lead before substitute Olivier Giroud’s 89th-minute header cost Jose Mourinho’s side what would have been only their third Premier League victory since August.
United have been frustrated at home this season, with the draw with Arsenal the latest game they have dominated without winning, after failing to take all three points against Stoke and Burnley in October.
The result left the Red Devils in sixth position, nine points adrift from leaders Chelsea and six points off the Champions League spots.
And Mata knows they would be among the teams currently occupying a top-four spot had they managed to make the most of their possession in games.
"That frustration after the final whistle is not new, unfortunately,” said Mata.
"Against Arsenal we played yet another game where I felt that we did everything, or almost everything, to win and two points slipped away.
"The whole team did a great effort. We had chances, we were solid defensively to keep such a good team like Arsenal away from our box. We were one goal ahead in the 89th minute… and we got a draw.
"It could have been a great weekend and it leaves a bad taste, but we must be positive.
"The way we played, the motivation, ambition and competitiveness that we showed, or the team's personality are enough reasons to believe that sooner or later we are going to get the reward that we deserve.
Manchester United vs Arsenal player ratings
Manchester United vs Arsenal player ratings
1/22 David de Gea - 4 out of 10
With Arsenal scoring their only shot on target, it’s not been the best day for the Spaniard. He had very little to do throughout.
2/22 Antonio Valencia - 8 out of 10
Performed exceptionally today, looking strong going forward and defensively.
3/22 Phil Jones - 5 out of 10
Did the simple stuff well at the back, but looked slow defensively at times.
4/22 Marcos Rojo - 6 out of 10
Defended well throughout proceedings, played safely and used possession well from the back.
5/22 Matteo Darmian - 5 out of 10
A mediocre performance from the Italian. He was lunging into challenges, despite already being armed with a yellow card.
6/22 Michael Carrick - 5 out of 10
The skipper played a very standard performance today. He played his role well and stuck to his position.
7/22 Ander Herrera - 7 out of 10
His work rate was faultless and he influenced play in the middle of the park – good overall performance.
8/22 Paul Pogba - 6 out of 10
He appeared to patrol the middle of the park in the first half, but in the second half he seemed to go off the boil. He did not make many chances and lacked any attacking prowess.
9/22 Juan Mata - 8 out of 10
An exceptional performance from the Spaniard today. His goal was an example of his immense technical ability and he created chances throughout.
10/22 Anthony Martial - 6 out of 10
A somewhat quiet performance from him today, but he showed glimpses of brilliance in the first half with a number of strikes that tested Cech.
11/22 Marcus Rashford - 6 out of 10
Despite being caught out for the late Arsenal goal, his performance throughout was positive. He attacked confidently and his crossing was inviting problems for the Arsenal defence.
12/22 Petr Cech - 6 out of 10
He made a number of important saves in the first half, but was out of position when Mata broke the deadlock.
13/22 Carl Jenkinson - 4 out of 10
It was a somewhat uncomfortable performance from him today, as he looked slow and unable to keep up with the pace of the United strike force.
14/22 Laurent Koscielny - 6 out of 10
He did well in the air today, but the United attack got the better of him at times as he was caught out of position.
15/22 Shkodran Mustafi - 5 out of 10
It was an incredibly mediocre performance by the German. He did well in possession, but that wasn’t enough at times.
16/22 Nacho Monreal - 5 out of 10
A questionable penalty call in the first half was the main incident for the Spainard. He failed to show his defensive ability against the quality of United going forward.
17/22 Francis Coquelin - 6 out of 10
Made a number of important tackles, but it wasn’t enough to stop his opponents running the midfield battle.
18/22 Mohamed Elneny - 4 out of 10
The Egyptian made a few unneeded and mistimed challenges and failed to show any sign of threat when going forward.
19/22 Aaron Ramsey - 5 out of 10
He had very little of the ball throughout, and when he did he failed to do much with it.
20/22 Mesut Ozil - 5 out of 10
Taking into account his huge talent, it was a rather dim performance. He failed to create chances and feed Sanchez which resulted in Arsenal having no spark going forward.
21/22 Theo Walcott - 4 out of 10
A very quiet performance from the winger today. He saw very little of the ball and was regularly caught playing too narrow which left Arsenal with no width to their attacks.
22/22 Alexis Sanchez - 6 out of 10
He looked dangerous when in possession, but a lack of service did not allow him to make a real impact on the game.
"Now we could talk about where we would be with nine points instead of three after those consecutive draws at Old Trafford.
"However, I prefer to focus on the idea that we must keep the same level and the good results will come.
"Sometimes the scores are difficult to take, but this draw is not going to stop us in our goal, which is to keep improving. There are still many games to play."Reuse content