Mata completed his club-record £37.1 million move from Chelsea on Saturday, and United have 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 will keep searching for ways to strengthen the squad he inherited from Sir Alex Ferguson, and admits they may have to wait until the end of the season to bolster their ranks.
"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."