Moyes broke United's transfer record to bring Juan Mata to Old Trafford last week and the Spaniard made an impressive start to his career at the club on Tuesday night.
Moyes conceded after the game that his team are still far from the finished article, but that does not mean he will be rushed into completing another big-money deal before the end of the window, however.
When asked about the possibility of any further signings this month, Scot said: "I would say no. I have said no, I don't think I will, but if something happens I will soon let you know."
Moyes was just as coy when it came to talk that Wayne Rooney is on the verge of extending his contract at Old Trafford.
"I am sure we will keep you up to date with that as well," he said.
On the basis of Tuesday's performance against Cardiff, the £37million United shelled out on Mata looks to be money well spent.
The Spaniard gave the midfield an air of calm fluency thanks to his energetic display just behind Robin van Persie.
The Dutchman evoked memories of his title-winning form last term when he pounced on a rebound from his own header to beat David Marshall in the sixth minute.
With substitute Rooney also returning to action after a four-week lay-off, Moyes thinks he has the ingredients to turn United into world-beaters again.
"The results with them (Rooney, Van Persie and Mata) will get much better," the former Everton manager said.
"We need to get them in the right physical condition now to make that happen.
"To see Robin van Persie and Wayne Rooney back on the touchline would have been enough to give everyone an uplift but then to have Juan Mata as well... He made our best chances in the opening 20-30 minutes so I was really pleased."
Cardiff impressed, but they still prop up the Barclays Premier League.
Manager Ole Gunnar Solskjaer, 11 years a United player, said: "I am pleased with our overall performance but we lacked that goalscorer who wants to score a goal, we lacked that oomph."
Solskjaer said a deal to sign left-back Fabio from United had been completed, but a loan deal for Wilfried Zaha has still not gone through.