The Red Devils came from behind to defeat Paul Lambert's men at Old Trafford, with Mata drawing the foul from Leandro Bacuna for Wayne Rooney to put the hosts ahead from the penalty spot, before the ex-Chelsea man slotted home his side's third goal.
It was the Spaniard's first for United after agreeing a club-record 37.1 million pound transfer from Chelsea in January and Moyes feels that it had been a long time coming.
"He's deserved it," the Scot told reporters. "His play has been very good. He's made a difference to the team, he's helped the team. Goals were one of the reasons we bought him. He's always scored goals, he's got a very good goal-scoring record.
"I think he was probably feeling it a little bit — he missed a chance in midweek, missed two good chances against West Ham — so I think there have been signs, the opportunities have been coming for him to score goals but, whenever he's played, he's made a difference and done very well for us."