The 46-year-old Uruguayan saw his team give Manchester City a scare in last weekend's Capital One Cup final before eventually losing 3-1.
He will head for Hull on Sunday knowing victory in the FA Cup sixth round will secure the Black Cats another day out in north London with a second appearance in a major final at stake.
However, Poyet is aware that the three league points on offer when Palace head for the Stadium of Light on March 15 could prove far more crucial in the context of the club's season.
Asked if he would be too disappointed to bow out of the FA Cup at the quarter-final stage, he said: "It's a good question, but I haven't even thought about it.
"I know Palace is a massive game, I can confirm that. I think it's bigger than any game we have played so far, including the cup final.
"Now this one is Hull and it's a week after, Palace, so it's not like it's two days after. We are going to use the squad the best we can and try to win the game.
"But there are a few games from now on and the position we are in the league, they become massive and Crystal Palace is the first one of them."
Sunderland will travel to Humberside still disappointed at the outcome of their Capital One Cup final adventure, but knowing they more than gave a good account of themselves.
Poyet faces the task of easing the pain of a near-miss, which left his players in understandably subdued mood.
He said "I read letters from people at Brighton when we were beating a Premier League team at half-time and it was the best moment of their life, and I thought, 'Oh my God', how you can make people feel.
"Imagine the Sunderland fans at half-time at Wembley? But we always say at the end of the day, it's about winning and we didn't.
"It was a strange evening at the hotel. It was a mix of yes, being proud, but sadness, but that's natural when you care and you don't achieve what was so close."
Hull completed a league double over Sunderland last month, but the Black Cats finished with only nine men at the KC Stadium on November 2 and 10 last time out.
Poyet said: "I think the team would like to go there and put a proper performance on - 11 v 11. If, at the end of the day, they are better than us, then we will take it."
Poyet, who will have midfielder Liam Bridcutt available once again - he was ineligible for the cup final - was coy when asked about speculation that the club is about to appoint Hamburg technical director Lee Congerton as its new director of football.
However, asked about plans to replace the departed Roberto De Fanti, he said: "It's normal all over the world.
"Because you are not used to it, the words 'technical director', 'sporting director' mean 'devil', 'terrible'. It's normal.
"The most important thing is the relationship between that person and the manager or the head coach. It needs to be spot-on, it needs to be clear, it needs to be honest, it needs to be in the same direction.
"It needs to be special because if not, it's not going to work. It's about working together, understanding each other, knowing what is needed and doing your job.
"Apart from that, again for me, it's natural. I would take the situation, to work with someone in that role. It's natural, I am not worried at all.
"Now, if it's going to work or not, I don't know. I hope."