The Spaniard deflected Erik Pieters' cross past David de Gea in the Manchester United goal to give the Potters an early lead.
Mata then missed a guilt-edged chance to equalise when he shot over the bar.
Manchester United player ratings against Stoke City
Sat, January 21, 2017
Express Sport rates the Manchester United players' performances from their Premier League clash with Stoke City
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How did the Manchester United players rate in their clash with Stoke City?
And writing in his weekly blog, the 28-year-old revealed his frustrations.
He said: "The game left me with a bitter taste. Firstly, we didn’t win. We created chances to get the three points and it makes us mad to see that the ball just doesn’t go in.
Juan Mata had a difficult afternoon against Stoke
"It’s especially frustrating when you are so unlucky as to score an own goal, when you’re trying precisely to avoid that.
"Personally, I don’t remember when was the last time that I scored an own goal, in fact I believe this is the first one. I know it goes with the territory.
Juan Mata shoots over against Stoke
"You’re trying to stop the cross, the ball gets deflected on your leg, then again on the goalkeeper… and it’s a goal. It happens every week, this is part of the game, but when it happens to you it hurts. Anyway, this is football, and things like that may happen.
"I hope that all our unfortunate actions of the remaining games were condensed in those 45 minutes, and I also hope that the team (and myself) is going to have better luck (and better shot accuracy) in the following games. As always, we have to stay determined and motivated, and carry on."