Mata handed United the lead with a sweeping left-foot finish from Ander Herrera’s cut-back in the 68th minute, but Olivier Giroud struck late to equalise and share the spoils.
Speaking to Sky Sports after the final whistle, the former Southampton man spoke candidly as he took responsibility for Mata’s goal.
"I'm just disappointed [with Mata's goal] because my positioning on the goal was disappointing from my side of it," Walcott said.
"Because, defensively, I want to [cover that]. I've been doing that all season. I know that [Mata] was my man to get in there [and stop from scoring]. So from a personal perspective, that's very disappointing for myself.
"But the guys, they did well, and we managed to get that point that we deserved. Maybe in years gone by, we would have lost that game.
"We need to turn these draws into wins... But in years gone by, this is a very tough place for us to play and we managed to get a result today."
For United, Giroud’s late goal saw the home side held to a third consecutive league draw at Old Trafford.
Jose Mourinho’s men enjoyed the majority of chances, registering 12 shots, five of which were on goal, but struggled to convert this dominance into three points.
Giroud’s headed goal was Arsenal’s only shot on target throughout the game and Mourinho insisted afterwards that his side had been unlucky not to walk away with three points.
"I have nothing to say against my players, but I feel sorry for them because we feel like a defeat and Arsenal is feeling like a victory,” he said.
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.
"If we just focus on [draws against] Burnley, Stoke and Arsenal - nine points easily. If we had those six points more we are top four and close to the top of the league."
"We all know inside that in this moment we are the unlucky team in the Premier League."