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 Barclays Premier League win at St James' Park.
Manager 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, more importantly, assists as well.
"Over the last few seasons in the Premier League, Juan Mata is one of the best assist-makers and he has always got himself a good tally of goals.
"We needed that and he is coming up with the goods now."
Moyes made wholesale changes for the trip to Tyneside with only three of the men who started against Bayern Munich in midweek - Phil Jones, Antonio Valencia and Marouane Fellaini - retained with one eye on Wednesday's Champions League quarter-final return leg.
However, once Mata had fired them ahead from a 39th-minute free-kick which Magpies boss Alan Pardew felt should never have been awarded, they never looked back.
Mata added a second from close range five minutes after the restart and Javier Hernandez put the result beyond doubt 15 minutes later, before substitute Januzaj wrapped up a comfortable win at the death with the help of a deft assist by the Spain international.
The win lifted United into sixth place, with Tottenham not in action until Monday evening, but Moyes refused to be drawn on the prospect of a Europa League campaign.
He said: "The job I would like to do is finish as high up the table as we can.
"I don't know where it's going to be, I don't know what's going to happen, but I want to try to keep winning the games and see where we end up.
"If we get into that situation, then we can make a call on it."
In the meantime, Moyes will turn his attention back to the Champions League and was hoping for good news on Wayne Rooney's toe injury on his return to the north-west.
He said: "I have not heard today from the medical team back at Carrington, but we are hoping it will be making progress.
"He's a really important player for us and we will give him every opportunity to be right with his toe."
Opposite number Pardew was in subdued mood as he reflected upon a seventh defeat in 10 league games - Newcastle have conceded 11 goals without reply in the last three - as a season which at one point promised so much continues to unravel at an alarming rate.
He said: "It's tough
I understand the fans' frustration
They want to see exciting football at this stadium and we are just not producing it at the moment.
"We need to just gather ourselves together and hopefully go to Stoke and put on a performance which is above the last three.
"I thought the commitment was on the pitch, there was a lot of good commitment
We actually had some decent performances in and around that performance, but United were too good.
"The last few results, particularly the last three, have been tough, tough games for us.
"The opposition have been above us, there's no doubt about that, and we have not really had any breaks in the games.
"We had chances
The first goal was essential for us, I thought, and we didn't get it."
Source: PA