Old Trafford boss Moyes smashed his club's transfer record during the January transfer window to bring Mata to Manchester from Chelsea.
The Spain international failed to find the net in his first nine appearances for the reigning champions but opened his account in last weekend's 4-1 home triumph over Aston Villa.
He doubled that tally with a sublime first-half free-kick at St James' Park, added a second after the interval and rounded off matters with a cute backheel that allowed Adnan Januzaj to complete the scoring.
"I think Juan Mata's played really well and I think he's made us better," Moyes said.
"He hasn't had the goals in the early games but I think he played fine. Recently he's started getting the goals and, more importantly, the assists as well.
"I think, over the last two seasons in the Premier League, Juan Mata was one of the best assist-makers.
"He's always got himself a good tally of goals and we needed that. He's coming up with the goods now."
Moyes also paid tribute to Mata's co-star in the creativity department, Shinji Kagawa.
A lack of game time for the former Borussia Dortmund star has been a source of frustration for sections of the United support.
However, Japan international Kagawa was handed a chance on Tyneside as Moyes made eight changes to the side that drew 1-1 with Bayern Munich in the UEFA Champions League on Tuesday night - casting an eye towards next week's return leg in Germany.
"Shinji played well," Moyes added. "Maybe a bit slow at the start but I thought as the game gathered momentum he was influential."
