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.
"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."
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