Hull needs a victory to stay alive in the relegation battle when they visit Selhurst Park this weekend.
Marco Silva's Hull, currently 18th in the league and one point adrift of safety, could face the drop if results do not go their way this weekend.
Allardyce wants 16th-placed Palace to seize their opportunity to steer away from the relegation battle in the penultimate week of the season.
"It's all about getting the result," Allardyce said.
"If we can through playing well and scoring goals then great but if we need to play ugly, play ugly.
"It's another opportunity for the lads to clinch survival. I've said: 'How many opportunities do you want? Take this one!'"
"The pressure lies with Hull. They have to win, we only have to avoid losing."
Palace have lost their last three league games and will hope winger Wilfried Zaha can add to his tally of six goals for the club this season.
With the opposition recently trying to nullify the 24-year-old Ivory Coast international's impact on the game, Allardyce has urged Zaha to stick to gameplan and avoid getting frustrated on the pitch.
"I can't affect whether referees protect Wilf," Allardyce added. "If Wilf doesn't get frustrated and keeps running at defenders he'll draw fouls.
"He was fouled three times in one phase of play against Burnley [last month]."
