The survival specialist arrived at The Hawthorns last week with the aim of keeping the club in the Premier League.
Allardyce has an outstanding record when it comes to battling the drop, with the 66-year-old having previously defied the odds to keep the likes of Bolton, Blackburn, Crystal Palace and Sunderland in the top tier.
Albion are currently five points from safety, but the Dudley-born boss is adamant he can once again produce a dramatic escape.
However, he admits there are no guarantees and he says losing his title as the man who always keeps teams up would be a crushing personal blow.
“I think the never having been relegated thing – to lose that would kill me if we did go down,” said Allardyce who has signed an 18-month deal at The Hawthorns. “I’d be massively upset.
“If I stay at West Brom and get them back up, that might be a relief from that – to get them back up again.
“But I would still have that tag of having got relegated with one club so I don’t want it if I can help it.
“It may happen this time, I can’t guarantee it won’t happen. But I will do my absolute best to get us safe.”
Allardyce’s appointment as Albion has seen his career go full circle.
The former Bolton boss actually began his coaching career at The Hawthorns as player-coach of the club’s reserve side.
He was then promoted to be Brian Talbot’s assistant manager before the pair got sacked following an FA Cup loss to Woking.
From that point, he worked his way through the leagues to go on and become one of the best managers in the country.
But he said he will never forget his first coaching session at Albion, with Allardyce quickly learning all managers have to think on their feet.
“The first training session at West Brom I was an absolute bag of nerves,” he revealed. “That training session was as the player/manager of the reserve team – because I still had a player’s contract then. I was extremely nervous about what the players thought about me.
“It was really important that I tried to get their attention and keep them on board and try to get them to enjoy the session. It was a great challenge to see if I was good enough to move from a player to a coach.
“I had done all my badges. But I always remember I planned the session, I’d asked Brian the day before how many players I had.
“I had 16 and I had planned for 16. Then in the morning, he said I only had nine because he needed the others.
“I was thrown right into the deep end but it actually taught me to think on my feet more. The session I had planned went completely out the window.
“I had to train nine players for an hour and a half and most of them were pretty annoyed because they hadn’t got the call to be involved with the first-team. That was a great learning curve.”