The result leaves the Hammers two points above the dropzone.
Nuno said afterwards: "That was a tough match, always is against Palace. We had some good moments in the first half and it started to go a bit side-to-side in the second half.
"A very tough, balanced match. It could have gone both ways."
Asked if the relegation battle will go to the last day, Nuno also said: "It will go all the way, for sure. Not only at the bottom of the table but at the top. This season has been very tight.
"We don't make points, we play games. We have a mission ahead and keep going."
He also said: "We performed well. We were organised and compact. Tough match. Our offensive process, the combinations didn't quite go - the final ball, the final touch.
"The game was very balanced.
"It's a tough shape to play against. It's brought them a lot of success. It's hard because they are good players. You cannot find the gaps. They are a threat on the counter-attacks.
"We were solid. It's going to be a fight until the end."