The sides meet at the Stadium of Light on Saturday with the Black Cats still four points from safety despite winning two of their last three league games, and six adrift of the Cherries in 15th.
Victory for the home side would drag Eddie Howe's men back into the thick of the survival scrap, but anything else would compound Allardyce's problems.
He said: "At all costs, we cannot lose this game, for me
We must try to win it if we can, but if we can't, make sure we don't lose it because the distance then between Bournemouth and us, even though people say there are a lot of games to go, there aren't.
"To make up that difference, there isn't
When you are at the bottom and you have only won five already, you are saying you are having to win three just to catch them up, so we cannot afford to lose this game.
"Hopefully we will win it, but if we don't, make sure we don't lose.
In Sunderland's favour is the fact that their two most recent successes have come against fellow relegation candidates Aston Villa and Swansea.
However, they are yet to draw any of the 15 games for which Allardyce has been in charge to date - they have won five and lost the other 10 - and that is a statistic which continues to perplex the manager.
He said: "They have done one good thing - win five - in the short period of time I have been here
The only thing is they haven't done the other thing very well, which is draw games that they shouldn't have lost and made sure they should have drawn.
"Had we done that just on the extra points, we'd probably be out of the bottom three - in fact, I know we'd be out of the bottom three."
It is no coincidence that the Black Cats' wins over Villa and the Swans came in part courtesy of five goals from striker Jermain Defoe, although Allardyce admits they cannot continue to rely solely upon their 33-year-old frontman to get them the points they need.
He said: "Somebody else has to have their shooting boots on
It can't always be Jermain."
Bournemouth will head for Wearside on the back of a precious 3-0 victory over Norwich with manager Eddie Howe knowing back-to-back victories could ease them well clear of trouble.
Allardyce said: "Eddie has been progressing steadily over a few years now, even though he still looks very young and handsome and not as haggard as most of us when we do this job.
"His experiences over the years have shown that he's very competent as a manager and now he's at the top level of his industry, so it's great credit to him and the club as a whole on what they have achieved."
Source : PA