Victory over faltering Everton at the Stadium of Light would ensure the Black Cats' continued presence in the top flight after a fourth successive late escape, something which was far from certain before Saturday's fine 3-2 win over Chelsea.
However, while manager Allardyce insists his players would deserve to celebrate, his response would be more low key.
The 61-year-old said: "I think it will be a big celebration for the players - and I think they should go out and celebrate as well if they can do it.
"But for me, it would be a huge relief to have achieved it in what's been a very, very difficult season for us all. We have managed to put the club in a position to try to build from where we are."
Allardyce answered owner Ellis Short's call to arms in October following Dick Advocaat's departure and while there has been significant improvement, his mission has gone down to the final week of the campaign, much as he expected it to.
However, should his side ease itself over the finishing line, that would spare him the ignominy of having to add a first top-flight relegation to his curriculum vitae, a secondary concern for the former West Ham and Bolton boss, but a concern nonetheless.
Allardyce said: "It's not as important as the club staying in the division. It's more important for the football club than it is for me.
"Yes as a manager, you don't want a relegation put on your CV, but you work for the football club and it's about keeping the football club safe and then if that's the case, then we're both okay, aren't we?
"My CV still says there's no relegation from the Premier League on there - in fact, I've only ever suffered one relegation, with Notts County where I didn't take over until late January or early February, so in terms of my management career, it's been pretty good at avoiding relegation all the way through.
"Hopefully there'll be no blemish on it by the end of the season."
Everton will arrive on Wearside with manager Roberto Martinez's future a topic of intense debate amid a run which has seen them win just once in nine games, culminating in Saturday's 3-1 defeat by champions Leicester.
However, Allardyce believes that and what is at stake for his club increases, rather than reduces, the pressure on his players.
He said: "Knowing that we can do it in that one game with a win and can kill everybody else off is pressure in itself to say can we produce a big enough performance to do that?
"Of course our opponents will be there to challenge us and there to spoil our celebration, so we have to bear in mind that Everton will come and fight all the way because of the criticism that they received on the performance against Leicester.
"I can't see anything other than a reaction to that from Roberto and his players on Wednesday night and we need to be really on top of our game."