Two first-half goals from Danny Welbeck and a Tom Cleverley strike early in the second period were enough for United to claim their first league win in over a month.
And, whilst Moyes insists that the performance at Villa was not much different from their previous two games - losses to Newcastle and Everton - he admits improvement is still needed.
"I don't think there was an awful lot of difference [in the games], except we obviously scored the goals," he told Sky Sports.
"We have not been scoring and goals change how it looks, mainly for the media, but we know we have to play better as well and we have to play better than we did today again. It continually has to improve and I will make sure it gets better over the coming months.
"I think we will play much better, I have told the players that is the least we can do and we have to keep going and win more games."
He was pleased with the performance as a whole and added: "It was a good job done, the players played well and the only thing I could be critical of was that we didn't score more goals.
"Antonio Valencia was very good and young Adnan [Januzaj] is still learning his trade and will be a really talented player in the future. We played well but were a little bit sloppy in the opening five minutes or so but after that I thought we played really, really well."
He was also pleased with his two goalscorers and said: "Danny Welbeck is someone who we know he needs to keep scoring goals, he was good today and was a threat and could have had more today.
"It would have been nice for him to get a hat-trick but two is a good tally for him.
"Tom has been playing okay and today I thought he played really well, passed it well and took the ball and ended up with a goal from midfield as well."
I've already said that @leixlipgooner isn't an Arsenal fan he's/she's a United fan. He/she has no interest in Arsenal at all. He/she has a fanatical (the word "fan" is derived from) hatred/jealousy of United's success and also is desperate for attention so writes ridiculous antagonistic comments on the united threads of this site. This is the last time I am going to rise to it and everyone else should stop responding too because its exactly what he/she wants, as it gives him/her an unjustified sense of importance in his/her tiny pathetic existence. Stop responding (and I know there is plenty of irony in this comment given this is a response) and he/she will eventually recede into his/her pathetic little isolated and pointless existence. On Arsenal generally (and I actually had hoped they¿d do well this season as a lot of Arsenal fans have given Wenger some unfair flack), the sad reality is they have no chance of winning the PL this season and it is not impossible that after next weekend they will have dropped out of the top four, never mind be top of the league. To be fair apart from @leixlipgooner I¿ve not seen too many Gooners singing from the from the roof tops just yet.- eric'sballs