Mata completed his club-record 37.1 million pound move from Chelsea on Saturday, and United has been actively seeking further additions, opening preliminary talks with Southampton for Luke Shaw and scouting Bayern Munich duo Toni Kroos and Dante.
But Moyes does not expect to add to his side any further this month, though he will keep searching for ways to strengthen the squad he inherited from Sir Alex Ferguson, and says the team may have to wait until the end of the season to its their ranks.
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"I hope it will be the first of some new signings that will arrive, but more likely in the summer."
United has struggled in the Premier League this season and is 14 points adrift of leader 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 soccer 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."