An SAS soldier, Nigel Ely, had set a reserve of £250,000 for Hussein's 2ft-wide bronze buttock.
The 22-year-old, who used a sledgehammer and crowbar to acquire the memento, had planned to give the proceeds to charity.
But the highest bid stood at just £25,000, coming from a bidder from New York.
Auctioneer manager Charles Hanson admitted his surprise at the fact the statue piece did not sell for more.
"When it comes to modern history, freedom and liberation, it's very important - it's normally something money can't buy," he said.