The Black Cats host Crystal Palace on Tuesday evening still smarting from Saturday's 1-0 defeat at West Ham, during which they created more than enough chances to get something from the game, but ultimately left Upton Park empty-handed.
As luck would have it, they ended the weekend no worse off with fellow strugglers Aston Villa, Norwich and Swansea all losing and Newcastle not in action, although that provided little comfort to their 61-year-old manager.
Allardyce said: "It doesn't matter. Twenty-three points, 27 games - if the season finishes now, we are relegated, so you have got to get to 38 points or better, it's as simple as that.
"It doesn't matter what anybody else does, you have got to go and do it yourself. You can't rely on others, you have got to do it yourself.
‘Bully’ broke disabled girlfriend’s arm and dragged her through broken glass in shocking campaign of cruelty
The 16 places where most crime was reported across South Tyneside in June
13 great pictures as the sunshine sees crowds flock to South Shields beaches
‘Sinister’ paedophile watched children play and offered them doughnuts after moving into new neighbourhood
South Tyneside man given jail warning after breaching court order
"If you rely on others, you'll get relegated."
Sunderland have just 11 games remaining in which to dig themselves out of trouble for a fourth successive season, and Allardyce has set them a target of five victories to give themselves a chance.
He said: "We have got 11 games and we have got to have our best run of the season.
"We have got to pick up five victories if we can in 11 minimum, and that's 38 points in the hope that 38 points is going to be enough again this year."
The Black Cats boss has repeatedly bemoaned his side's inability to keep clean sheets - they have not done so since November - and he knows that will be a challenge once again this time around with Yannick Bolasie, Wilfried Zaha and former Sunderland frontman Connor Wickham at opposite number Alan Pardew's disposal.
Palace are currently in the midst of a 10-game run without a league victory and defeat at the Stadium of Light could drag them to the fringes of the relegation battle, although Allardyce believes they are safe.
He said: "He [Pardew] has gone 10 games without a win, he has just slipped into the bottom half for the first time and there are only 11 games left, so it shows you what it means when you get off to a very good start in the season.
"Those mid-table teams or teams who are struggling at the bottom can always have a run like that, but if you have put it right in the first place by getting off to a great start, then you're okay, you're all right."