State Sen. David Ige trounced Abercrombie in Saturday's Democratic primary, with 66 percent of the total. Abercrombie received 31 percent.
The vote was held Saturday as parts of the island chain coped with power outages from Tropical Storm Iselle. Voting had to be postponed in some precincts.
That means the race between Democratic U.S. Sen. Brian Schatz, who replaced the late Daniel Inouye, and U.S. Rep. Colleen Hanabusa is still undecided. Schatz had
113,800 votes or 48.5 percent of the total while Hanabusa had 112,165 or 47.8 percent.
Hawaii is a Democratic stronghold so the winners of the primary are likely to win November's general election.
Abercrombie conceded Saturday, sending a tweet: "No regret. Every waking breath has been for you, Hawai'i. I have given all I can every day I can."
At 76, Abercrombie was the second oldest sitting governor after Jerry Brown of California. He had a long political career that included stints in the state legislature before he was elected to Congress in 1990, serving there until he ran for governor in 2010.
Inouye, as he was dying, urged Abercrombie to name Hanabusa to his Senate seat. While Abercrombie instead named his lieutenant governor, Schatz, Hanabusa campaigned as Inouye's true successor.
"It is far from over," her campaign account said via Twitter early Sunday.
President Obama, who grew up in Hawaii, endorsed Schatz in the primary.