Palace managed to keep a rare clean sheet in an away win at Bournemouth last month but then suffered a horror show in a 4-0 home defeat by Allardyce's former club Sunderland a week ago, conceding all four goals before halftime.
"I thought we turned the corner at Bournemouth," he told a news conference on Friday. "But Saturday at home, it was like a hot knife through butter -- wide open, no defensive solidarity.
"We did what we had to do, as early as we could, in terms of addressing the issues of last week. We've got to take it on the chin and bounce back. We've got to show some real fighting spirit which everyone wants to see."
The Sunderland defeat left Palace second bottom in the Premier League, with the 2-0 victory at Bournemouth their only league win since Allardyce replaced Alan Pardew in December.
"I haven't been relegated from the Premier League in my entire career, so it's the last thing I want," he added.
"This team has a great chance of survival.
"I keep preaching the same thing: if you can't win, don't lose. But we keep losing! We need to get a result, and have got to pick points up."
(Reporting by Steve Tongue; Editing by John O'Brien)
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