The Blues are unbeaten away in the league since Moyes replaced Sean Dyche and the Scot admits the squad has surprised him.
Everton go to Wolves on Saturday with the Blues appearing safe from a late season relegation battle.
Moyes said this morning: "I think they have (surprised me).
"I think now we are seeing players who are stepping up to better levels, we have shown some consistency with what we have done and the next step is can you keep it going.
"Maybe the secret is that we've had more home games than away games. I have to say that our run of games - we've had quite a few home games and Goodison at the moment is special.
"I have to say that we've been away to Brighton, Crystal Palace and Brentford and the players have done a really good job. We have to try and keep it going, keep improving and making progress."
However, while delighted with the Blues form, Moyes insists they're not yet safe from the drop.
He continued: "We have to always work on what could happen but I think at the moment we are trying to see if we can get a little bit better in every game and play a bit better and do better things. The players have done a remarkable job in the last 5/6 weeks but I'm not thinking we're safe, that's for sure. We have to keep getting points."
Everton meet Wolves at Molineux at 8pm on Saturday night - a time which is unusual for Moyes.
He joked: "I'm normally a bottle of red wine down by that time on a Saturday!
"If you're a traditionalist then you probably don't see 8pm on a Saturday night as a good kick-off time but it's the way it's going and I think football clubs are signing up to it due to the money that is coming in from the broadcasters. We have to go with it even if it will ruin some people's Saturday night out."
Moyes also delivered an upbeat update on Seamus Coleman's return to full fitness. The veteran fullback and club captain was in Dubai with the rest of the squad for last week's warm weather training camp.
Coleman is recovering from a calf strain and Moyes added: "Seamus Coleman, Armando Broja and Youssef Chermiti are all getting themselves closer to getting ready to play again.
"Whether Seamus is ready to be involved I'm not quite sure yet, he's still training and we're trying not to get him re-injured. We will give him every opportunity to make sure he is fine."
Another club stalwart was raised in the media conference, with Moyes full of praise for the impact of former club captain Leighton Baines. The once left-back has stepped up from the academy to act as one of Moyes' coaching assistants.
The manager said: "He has great insight... I think he is enjoying working at the top end. He is helping a lot."