Second-bottom Albion are 11 points from safety and looked destined to drop into the Championship with only 13 games left to climb out of the relegation zone.
Allardyce, 66, has kept the likes of Sunderland, Bolton and West Ham in the top-flight in the past. But the former England boss has not had the impact many expected since taking over at The Hawthorns in December.
Albion have taken three points just once in 12 Premier League games under Allardyce and they are currently on a dismal seven-match winless run. Despite West Brom's struggles under his watch, the ultra-confident Allardyce refused to accept he would be blamed for their likely relegation.
"I'd be devastated from a personal point of view, and for the club not to have survived the first season back at this level, for when the fans come back," Allardyce told reporters on Thursday. "Personally it would affect me, but it might not affect my credibility too much in terms of people know what I can do. If you're established as a manager other jobs come along. That's not what I want to achieve at West Brom, but it's what might happen.
"I won't be happy, the club won't be happy because I've not done what they wanted me to do, and the players won't be happy because they'll get heavy reductions in their salary."
West Brom spent two seasons in the Championship after being relegated from the Premier League in 2018. Slaven Bilic led them to promotion last season, but the Croatian was sacked two months ago as Albion turned to Allardyce.
West Brom start a run of three home fixtures against fellow strugglers Brighton on Saturday, with Everton and Newcastle also visiting in the next week.
"There is time, but we have to get on a run of games of a top level we haven't achieved this season," Allardyce said. "We need to start hitting top-eight form. That's the reality."
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