West Ham needed extra-time as Crysencio Summerville struck for the 1-0 win at Burton today.
Nuno said afterwards: "I'm very pleased that we achieved what we came here for – to go through.
"Let's see how where we can go in the competition, day by day. Let's wait for the draw on Monday. We knew that it was going to be tough, but I think we did a good job.
"Every set piece from Burton (was going to pose a) problem and they were focused. Thank you to our fans who were amazing in supporting us through all the game, coming so far, and it being so cold.
"I think, like you said, it’s job done. Let's now recover the boys and prepare for the next one."
Nuno also stated, "Burton put a fight and this is the FA Cup.
"We knew what to expect and Burton came out strong. I think we worked the game out, we controlled it, and then in the second half it was all about us trying to get the spaces where there were not many spaces.
"But we achieved a beautiful goal in extra-time and (got the) job done."
He added, "We go day by day and let's see how far can we get.
"But the ambition is to go day by day, improve the players, and be ready for what we expect. The draw is on Monday, we'll wait and see.
"The atmosphere is good. The boys are working hard. You just see them pushing themselves. We're going to need them all. So, thank you again to the fans. They were amazing."