The defender opened the scoring from distance before dispatching a penalty as the Toffees held on following Shane Long's goal for the Baggies, and Moyes expressed his belief that the Merseyside outfit are fortunate to have the 28-year-old.
"I thought he played really well. He keeps getting better," he told reporters.
"When teams try to stop him he tries to work on ways to alter doing things. He’s great for a manager because he wants to get better himself and he wants to keep improving so we’re very fortunate to have him here.
The former Preston boss also praised his side's resilience as they saw the final 30 minutes of the game out following the visitors' consolation on the hour mark.
"We needed a second goal just before half-time which made things a lot easier and probably changed the way West Brom were thinking," he continued.
"We gave away a really poor goal but apart from that we hadn’t done an awful lot wrong all night really. I’m pleased with the performance and the games in the Premier League are tight; you don’t get much from any teams and you’re going to have to earn it."
Moyes went on to underline the difficulties of completing transfers after the club missed out on the signing of Feyenoord midfielder Leroy Fer this week.
|5/1||Leighton Baines is 5/1 with Coral to score anytime in Everton v Aston Villa
"There are lots of things which are connected to signing a player. It can be the contract, the agent, the clubs and medicals as well. All those things play a part and on this occasion some of them didn’t quite come together.
"I don’t know if we’ll be doing anything [in January]."
West Brom coach Steve Clarke, meanwhile, bemoaned his side's concession of two goals in the first half, claiming the visitors had given themselves a mountain to climb.
"If we’d have gone in 1-0 down we’d have had more chance of getting something from the game. I don’t think we were great [in the first half] but I didn’t think Everton were great either," he said.
"I thought we were quite comfortable in the game and then we gave away a bad goal which made it 1-0. Even after that I thought we were still in the game, but the penalty on half-time made it much more difficult."
|"I don't think we were great but I didn't think Everton were great either. We gave away a bad goal"
- West Brom boss Steve Clarke
The former Liverpool assistant boss also revealed that George Thorne is likely to face a lengthy lay-off due to the knee injury he picked up at Goodison Park - and hinted at late transfer business as a result.
"George has hurt his knee. He’ll go for a scan and we’ll find out the scale of the damage. Fingers crossed for the player himself it’s not too much but at the moment it doesn’t look very good," he said.
"We’ve only got tomorrow to do it [sign players]. It was never in our plans to bring new faces in this window, we wanted to keep the squad we’ve got.
"It’s something we’ll have to discuss and hopefully we can get a late night meeting or early morning and sit down and discuss it and decide what’s best for the club."