The Hammers set up the win with goals in the first-half from Crysencio Summerville and Taty Castellanos.
Nuno said afterwards: "The boys did really, really well. They were committed, desire, organised, talent up front, nice goals, nice combinations and a clean sheet that makes us proud of the way we defend. Because I believe that everything starts from there. If we can fix it, then up front, we have talent that can help us.
"(It’s because of) talent, talent, talent (that we’re scoring so many early goals). We knew how important it was to start the game well.
"From minute one, we were switched on, on the front foot, we press, we recover balls, we went. We didn't allow too many situations to Burnley. That makes a big difference, makes a big difference.
"Today, we managed the game well. It was a spell during the second half in the beginning that Burnley put us against the ropes, but then came our fans singing and helping us. I'm really happy for them to make this travel so far away on a rainy day and help us today.
"We cannot thank them enough. Let's try to put this energy into London Stadium on Tuesday."
The manager also said: "There's no individuals. We need the best of each one of us. That's the only path that you can take.
"It starts from there. We are aware of the problems that we've been having. We have to solve it, we have to fix it.
"Individually, the players in defence were OK, but it's more about the line, the way we can connect with each other, covering spaces. We did well, we did well, we did well.
"Like I said, a clean sheet. Moving forward, it's important, it's important. We knew that today was going to be very, very tough, but everything starts from there, our organisation when we press.
"So, congratulations to the boys because they did an amazing job today."