Sam Allardyce insists the "pressure lies on Hull" when they visit Crystal Palace for a fixture that could define each team's season.
Marco Silva's side could be relegated if rivals Swansea win at Sunderland on Saturday and Palace avoid defeat to preserve their Premier League status.
Allardyce had long believed 38 points - Palace's present total - could prove enough to avoid relegation but now knows that a draw against their under-threat opponents would guarantee survival.
A poor result could instead leave them requiring an unlikely victory at Manchester United on the final day of the season, but considering Hull's greater need he insists his players' priority is to remain calm and avoid a fourth straight defeat.
"The pressure lies on Hull. They have to win the game, we have to draw it," said Allardyce, 62.
"If we are defensively very sound and solid, like we were against Arsenal (in last month's 3-0 win), we are bound to create some chances at home and hopefully score.
"We play not to lose - that is the key element. It's been extremely difficult in the last three games. Hold your nerve on Sunday for one and make sure you produce your best performance and if that's good enough, then that's great.
"There is Hull we need to compete against, and the size of the game. Whoever deals with the pressure better is a big factor.
"Our crowd will be a big help as long as they get don't nervous. If they get nervous, they can pass that over and that will make us a bit more nervous. We have to deal with the emotion of the game on Sunday and come out on top.
"The clean sheet is all important. If we don't concede a goal, we stay in the Premier League.
"(The mental aspect of football) is one of the biggest parts of whether we succeed. Your football intelligence on the day decides whether you play well.
"Physically they are fit enough and if they hold it together mentally, stay positive and deliver the best performance, that will be good enough."
Allardyce will await the results of late fitness tests given to James Tomkins, Yohan Cabaye and Scott Dann before he selects his XI to start at Selhurst Park.
An injury to the on-loan Mamadou Sakho has left Palace short in central defence and done much to disrupt the positive momentum they had built, similarly to that seen at Hull since Silva's appointment, and Allardyce said of the Portuguese: "(He's been) excellent.
"Like everybody else, like here, the recruitment of players has been the difference between us before January and us after January. We brought four in, they brought eight. Mick (Phelan, Silva's predecessor) before that never got that luxury.
"The managing of those eight players and putting them together so quickly deserves a lot of credit to the manager on how he's integrated the players and tried to fight their way out.
"I stick to the same philosophy as when I arrived here: if you can't win, don't lose. That philosophy has to apply for Sunday and whatever happens, however well you play or don't play, it's the result that matters.
"Get the result however we need to get it. If we can get it by playing well, being creative and scoring goals, then fine. But if we have to get the result ugly, we will get it ugly. That's all that matters on the day."