Sheffield Wednesday's defeat by Cardiff on Saturday means Palace can avoid the drop with three points against the promoted Baggies at Selhurst Park. It would be a significant achievement for a club who lost manager Neil Warnock in the wake of the move into administration and attendant 10-point penalty.
Hart said: "If these players manage to stay up it's a feat they should be revered for. It's massive. We've had a schoolboy on the bench, terrible injuries and 10 points deducted."
Hart will be hoping West Brom take their eye off the ball having already sealed promotion to the Barclays Premier League.
Indeed, Baggies boss Roberto Di Matteo is already planning for next season.
"I am very excited about next year," he told www.wba.co.uk. "I am looking forward to it.
"I think change is vital in life, not only in your professional life but also your private life. Change is always challenging.
"You don't really like it at first but you become accustomed to it - and it's good.
"I am looking forward to working with these players and some new players.
"I have enjoyed this year with this group. They have been very good, and the same will apply next year."