The Old Trafford boss was delighted with his side after they overcame the current league leaders and confirmed that Nemanja Vidic had travelled to hospital with a head injury
The Premier League champions picked up three points after a Robin van Persie header proved enough to overcome the current league leaders.
"It was a big result for us today," Moyes told Sky Sports.
"Arsenal have been playing well this season and we had to play well ourselves today to get the result.
"I thought we started the game well. I thought we were very good in the opening 30 minutes of the game. I thought our determination, our effort, our commitment and our good play helped us in the second half when we were under pressure.
"Overall it's three important points."
"I never thought anybody was going to run away with it [the Premier League]. I think there are a lot of ups and downs.
"It's a close run league this year.
"I'm pleased we're beginning to show a bit of consistency and a bit of momentum and let's hope we continue that.
Moyes also revealed that Nemanja Vidic, who was substituted at half-time with a head injury, was sent to hospital for scans.
He said: "He has gone to hospital. It was a terrible clash, it's an accident but hopefully he'll be ok, though I'll find out more from the medics later on."