Mata completed his club-record £37.1 million move from Chelsea on Saturday and Moyes believes that the signing of the Spain playmaker is the first step in his bid to build a side in his own image.
Southampton defender Luke Shaw and Newcastle midfielder Yohan Cabaye are just two of the many players who have also been linked with a move to Old Trafford this month, but Moyes does not expect any further additions before the transfer window closes.
However, the Scot is keen to continue strengthening the squad he inherited from Alex Ferguson, although he admitted that it would more likely be at the end of the season.
"I don't think we'll have any more in January," the United boss told the club's official website after confirming the Mata deal.
"I'm still working on it and looking to do things – we know exactly what we'd like to do and if it changes in the last week, which sometimes it can do, then we'll try.
"I hope it will be the first of some new signings that will arrive, but more likely in the summer."
United have struggled in the Premier League this season and are 14 points adrift of leaders Arsenal after seven defeats in their opening 22 games.
Mata is the first piece of the jigsaw for Moyes, and he has vowed to put a side together that is capable of moving them back up the table and delivering the style of football the club's fans have become accustomed to.
"I want to build an exciting team, that's always the way I've wanted my football to be played and I've not known it any other way," he added.
"I want to win and give the supporters something to shout about because I've not done that often enough.
"What I will say is that this is the first of many more to come in time. I'm looking forward to Juan being the start of it."
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