The 25-year-old Spaniard, a £37.1million capture from Chelsea, scored twice and set up Adnan Janujaz for his late strike as United cruised to a 4-0 away win.
Moyes said: "I think Juan Mata has played really well and I think he has made us better. He hasn't had the goals in the earlier games, but I really thought he played fine in the games. But recently he has started to get the goals and assists as well.
"Over the last few seasons in the Premier League, Mata is one of the best assist-makers and he has always got himself a good tally of goals. He is coming up with the goods now."
On a day when Moyes was without the injured Wayne Rooney, and decided to make eight changes to the side which drew 1-1 with Bayern Munich in midweek ahead of Wednesday night's return leg in the Champions League quarter-finals, United ran out deserved winners.
The win was not without controversy, with referee Kevin Friend coming under fire for awarding the free-kick from which Mata gave United a first-half lead. Newcastle's Dan Gosling was furious to be penalised for a trip on Darren Fletcher on the edge of the box, but as the home fans made their feelings known to Friend, Mata stepped up to curl a left-foot free-kick into the top corner.
However, there were no complaints thereafter as Mata extended the lead five minutes after the break and further strikes from Javier Hernandez and substitute Adnan Januzaj wrapped up the victory.
The defeat was Newcastle's fourth in five league games and there was little prospect of them completing a first league double over United since 1931 from the moment Mata struck.
Newcastle boss Alan Pardew was in subdued mood as he reflected upon a seventh defeat in 10 league games. He said: "I understand the fans' frustration. They want to see exciting football and we are not producing it. The first goal was essential for us, I thought, and we didn't get it."