Three goals in the final 20 minutes, two struck by the hosts, saw the Hammers edge this five goal thriller.
Nuno said, "It's very hard to win successive games in the Premier League and we've done it, which is really good.
"I think we can see some improvements in our boys. This is what we've been focused on individually, but we cannot (get carried away).
"There were moments, especially in the beginning of the game, that I think we didn't start well. We let Burnley have the ball, so it's hard to adjust. We can see it once again.
"It's a positive to react to the goal the way we did it, immediately with offensive actions, creating chances and scoring, but it's something that we have to look at as a team. It's not always going to be possible to react, so we have to try and change that situation.
"But overall, we're delighted for the boys."
Callum Wilson and Tomas Soucek struck and Nuno continued: "Both of those players you mentioned, Callum and Tomáš, they have this knowledge inside of the box to occupy the right spaces. I’m delighted.
"Callum, our striker, needs to score. His confidence is growing.
"It’s a good day for us, a very good day."
Nuno added, "I have to thank our fans, they were amazing.
"I always say, let's give them something and they'll give much more in return. That's why I'm humble enough to say ‘thank you so much’.
"We're going to need them again and again and again."