The 61-year-old saw his team bank another point - just their 19th of the season to date - from a 1-1 home draw with Bournemouth on Saturday when they desperately needed three.
However, defeats for relegation rivals Norwich and Newcastle and a draw for bottom-of-the-table Aston Villa meant the Black Cats were marginally better off at the end of the day than they were at the start, although still deep in trouble.
They remain in 19th place in the table, three points adrift of safety and with only 15 games left in which to rescue themselves, and the scramble for survival is never far from Allardyce's thoughts.
He said: "That's just the way it is, that's the pressure of the Premier League
You say, 'Don't do it', everybody does, you can't help it
It's 24/7 and as the season draws closer to the end, it gets more and more panicky because of the fact that there are this many points left in the games we have got left.
"It always gets worse when you go into single-figure games, that's even more pressure
That's why my hope is that we are at least close to level points-per-games when we get to the last eight games of the season."
On a positive note, Sunderland recorded their first draw in 16 attempts under Allardyce - they had won five and lost 10 of the previous 15 - and did so having recovered from an awful start during which Benik Afobe gave Bournemouth the lead with a 13th-minute header - their eighth goal inside the opening 15 minutes this season.
The early setback dented the black Cats' fragile confidence further, but they gained a foothold when full-back Patrick van Aanholt fired home an equaliser in first-half injury time.
Billy Jones would have given the home side the lead after the break but for a fine save by Artur Boruc, and substitute Lewis Grabban passed up a glorious opportunity to win it for the visitors late on.
Asked if Sunderland, who face both Manchester clubs and trips to Liverpool and West Ham in their next four fixtures, might have collected all three points if they had gambled, Allardyce was pragmatic.
He said: "Why? Why gamble when we have done it before and lost every single game? You don't gamble on situations like that, particularly when you have gambled before and ended up losing three and four and not gaining any points whatsoever.
"This is the first point we have gained from going a goal down since I have been here
Winning a game from going a goal behind is something that this club doesn't do very, very well if you look at the history of it, so to actually get a point is a good achievement from going a goal behind."
If Allardyce was happy enough with a point, opposite number Eddie Howe was disappointed that his men had not made the most of their early dominance, and although they sit four points clear of the drop zone, he is not content with their current situation.
Howe said: "That's a difficult one
From my perspective, I always want more and I set such high standards for the players that it's difficult to settle for where we are now
That's a tough question to answer.
"I think I'd have liked to have seen us higher."
Bournemouth's latest point came at an added cost with midfielder Junior Stanislas waiting to discover the extent of suspected medial ligament damage.
Source : PA