Saïd Benrahma's sublime second half goal was enough to secure a 1-0 victory in west London - the fourth win in a row that Moyes' men have put together this pre-season.
Moyes told the club's website: "We knew it was a tough test today, so I was pleased with how we dealt with it...
"I think we were quite good in the first half. We did some good stuff and I'm pleased because we're not at full tilt but we're getting there.
"We saw this as being a really tough game - probably tougher, even, than the game last week at Celtic - and it proved to be, and I'm pleased we got a result.
"We don't get carried away by the results, of course. I want to build a better team, I want to help build a better club all round, and the way to do that is by winning. That gives us a chance and hopefully we can keep it going.
"I'm delighted for Saïd scoring back here and we're hoping that's a sign of things to come.
"It was a good goal. He's been waiting on that one for a year, hasn't he? He practices it a lot and today he hit the target. Maybe it's fitting that he did it here.
"He also scored at Celtic last week and it's good to build his confidence in that way. We've got a lot of hope that he will get in and find his goalscoring touch, and assists and all those bits to do with his game. We want good competition and hopefully we'll have lots of people threatening to score goals this season."
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