Mr Rudd said he had already called Mr Abbott to concede defeat and to congratulate his successor.
"I gave it my all but it was not enough for us to win," BBC quoted the outgoing PM.
However, Mr Rudd and other senior Labor officials kept their seats, while another prime minister wannabe, billionaire and mining magnate Clive Palmer, appears headed for victory in the Sunshine coast seat of Fairfax after his party won over 11 per cent of the vote in Queensland.
Although the Coalition appears headed for a majority in the House of Representatives, the battle for majority in the Senate is still hanging.
Former Labor Prime Minister Bob Hawke blamed the Labor election debacle to divisions within the ALP with former PM Julia Gillard being ousted just a few weeks ago in a leadership spill and Mr Rudd reassuming party leadership.
"I really believe this was an election that was lost by the government rather than one that was one by the opposition," BBC quoted Mr Hawke.
Over 14 million Australians voted in the election since voting is compulsory in the country.