Christian Benteke's double secured a comeback win at Anfield which continues an impressive run for the south London side, who have now beaten Chelsea, Arsenal and Liverpool in recent weeks.
"Thirty-eight has been safe for a long time but we're not mathematically safe yet," Allardyce said after the match.
Palace's shock win on Merseyside took them up to 12th in the Premier League and seven points clear of the drop zone, but the Selhurst Park club face another tough test this week as they host second-placed Spurs, followed by Burnley, Manchester City, Hull and Manchester United.
Palace 'exposed Liverpool's weaknesses'
Allardyce thought his side exposed Liverpool's weaknesses in their win on Sunday, including Liverpool's continued vulnerabilities from set pieces.
He suggested that "on the corners everyone knows Liverpool are pretty weak."
"They conceded six off corners which we told the lads about. It's now seven off that corner that has got us the winner," he continued.
Allardyce also drew attention to his team's tactical awareness in the victory over Jurgen Klopp's men. Phillipe Coutinho had given the Reds the lead but two goals from former Liverpool striker Christian Benteke. Allardyce went as far as labelling the Eagles as "tactically exceptional". The former England boss said: "with our limited possession we exposed Liverpool's weaknesses time and time again and ultimately that has brought us from 1-0 down to win it."
However, with the game against Tottenham Hotspur coming on Wednesday night, Allardyce admits games against the top sides may be taking a toll on his squad. The 62-year-old suggested he "may have to make huge changes to make sure we compete with Tottenham."