By Laila Kearney

(Reuters) - Two men who say they mistakenly threw away a $1 million winning lottery ticket are suing the state of New Jersey to try to retrieve the funds, their attorney said on Thursday.

The two men, Salvatore Cambria and Erick Onyango, claim in a lawsuit filed on Tuesday in U.S. District Court in New Jersey that the state lottery failed to post winning numbers on its website in a timely manner, causing them to falsely think they had lost and to toss the ticket in the trash, attorney Edward Logan said.

"By the time they realized they won, the garbage had been taken away," Logan said.

Cambria and Onyango, who are neighbors living in Suffern, New York, had pooled their money to enter the $338 million Powerball jackpot, which was won in March 2013 by a convenience store owner.

The men's ticket, purchased at a 7-Eleven in Mahwah, New Jersey, had every number right except the Powerball digit, Logan said, and was worth a $1 million consolation prize.

When the men learned they had a winning ticket, they contacted the garbage company and the dump where their trash was hauled to, Logan said. They also considered hiring a bloodhound to sniff out the lost ticket, but eventually decided that the task of retrieving it would be impossible, he said.

Cambria and Onyango filed a claim over the missing ticket with the New Jersey Lottery Commission, and after waiting several months with no word back, they decided to sue, Logan said.

The men could prove they had the winning ticket because they purchased it in a package of three and Onyango kept the two tickets immediately before and after the winning one, Logan said. They also regularly played the same numbers at the Mahwah 7-Eleven store, he said.

Logan said lottery officials recently told him that his clients would not be able to claim the winnings without the actual ticket.

"In order to claim a winning ticket, one must possess a winning ticket," New Jersey lottery spokeswoman Judith Drucker said of the lottery's general rules. Drucker said she could not comment on pending litigation.

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Logan said his clients were "tremendously distraught."

"Could you imagine if you had a million-dollar ticket that you threw away?" he said.

(Editing by Leslie Adler)