But Palace have arguably the toughest run-in of any of the teams battling to escape the drop, with five of their remaining nine games against sides in the current top six.
“We’ve got a game midweek so I told the boys to enjoy the victory at home. No real time to celebrate. There’s still a way to go,” Allardyce told reporters.
Palace host Arsenal on Saturday and must also face Liverpool, Tottenham Hotspur, Manchester City and Manchester United before the end of the season.
“Never an easy game at our level,” Allardyce said. “We’ve still got City, United, Liverpool, Spurs, Arsenal, Leicester. Hull are in good form.”
Palace beat Southampton in the reverse fixture in December, but have lost on their last five league visits to St. Mary’s Stadium, and Allardyce is hoping his team can come away with a more positive result on Wednesday.
“You’d hope we could target a point, given the form we’re in. We have to be 100 percent. Every player was at their top level on Saturday.”
Allardyce praised forward Wilfried Zaha, who has scored twice in his last three games, but warned the 24-year-old not to lose focus.
“I’m very pleased with Wilf. He’s maturing as a person, producing consistent performances on the field. Hopefully Wilf isn’t listening to what the papers say, good or bad. I don’t want it to distract him.”
Defender Scott Dann may miss the rest of the season with a knee ligament injury, while Patrick van Aanholt (ankle) is still out. Striker Loic Remy is back in training after recovering from an ankle injury.
(Reporting by Aditi Prakash in Bengaluru; editing by Mark Heinrich)