The Baggies hopes of pulling off a great escape were dealt a hammer blow when they were ruthlessly swept aside by Leicester.
Goals from Jamie Vardy, Jonny Evans and Kelechi Iheanacho saw Brendan Rodgers side coast to victory at the King Power Stadium - a ground where Albion had never previously lost.
Allardyce's men offered very little over the course of the 90 minutes despite being Chelsea and Southampton in their last two outings.
But they did have a glorious chance to open the scoring early on when, just seven yards out, Mbaye Diagne completely missed the ball when he simply had to sidefoot it home.
That moment aside, though, the hosts dominated and should have won by a greater scoreline.
And Allardyce admitted his team now has a mountain to climb if they are to secure Premier League survival with the Baggies nine points from safety with just six games remaining.
"We are going to need five wins from six to be absolutely certain," Allardyce said.
"That would take us to 39 points which normally does it.
"Is four from six going to be enough? Maybe not.
"Leicester were far too good for us, in the first half particularly.
"We tried to look after their front two and one of the main reasons for our recent results has been our defensive solidarity.
"But Leicester tore it apart. We couldn't cope with them.
"We had a good chance to open the scoring but Mbaye Diagne missed his kick and those are the sort of chances we can't afford to miss.
"In the end, we thoroughly deserved to get beat.
"Was it great pressure from Leicester that forced us into so many errors? They are on a high, you can see why they are in the top four, they are as good as anyone in the league apart from Manchester City.
"Leicester are a lot better than Southampton and far better than Chelsea.
"You have to get the basics right and those basics deserted us."
Albion now face Villa in the derby on Sunday.
Both Allardyce and Dean Smith wanted to play the game last weekend - with both teams not in action.
But the Premier League refused with Villa now entering the derby having had 24 more hours to prepare after Dean Smith's side played Man City on Wednesday.
"We wanted to play Villa last Saturday, they wanted to play us but we weren't allowed to," Allardyce added.
"There is no need for us to play on Thursday and then Sunday. Why?
"Fine margins determine these games."