Arsenal dominated possession at the London Stadium but West Ham could have snatched the points when Javier Hernandez hit the crossbar late on.
Having led Manchester City before losing 2-1 and then beaten Chelsea 1-0, it was a third strong outing in succession against the Premier League's big boys and sets the Hammers up nicely for games against Stoke, Newcastle, Bournemouth and West Brom.
Moyes told BT Sport: "I saw the fixture when I took the job and I thought, 'Oh no, here we go'. But we've tightened up, we've not conceded any goals in the last couple of games, and we were a bit unfortunate against Man City.
"I want our football to be better, I want us to create better chances, but it's one step at a time.
"Against the better teams we've tried to make sure we don't concede, the other games might give us more chances to be on the front foot."
Captain Mark Noble was one of the standout performers and set up Hernandez's late chance, which saw goalkeeper Petr Cech possibly get the slightest touch to the Mexico striker's curling shot.
Noble said: "At the end with Chichi (Hernandez), he always hits the target but you would hope he would bury them, I think it was a good save in the end by Cech.
"They've got such a good amount of special players, you have to defend - simple as. Last year we got done here by the so-called bigger teams by three or four so to keep two clean sheets (and get) four points is a great reward.
"When you come out of the game against Everton away, where we lost 4-0, you go to Man City and you're dreading it, the position you're in.
"But we believed we could get something, Chelsea was a massive game for us and tonight to do it again, we just couldn't get that goal."