The laws, drawn up to ease Indonesian concerns after Australia granted asylum to 43 Papuans, would have sent all asylum seekers who arrived by boat to mainland Australia to detention camps on the remote Pacific island nation of Nauru.
But the prime minister dropped the laws in the run-up to Monday's vote.
Howard accepted that he did not have the numbers to pass the laws through the upper house.
Three government legislators defied him and voted against the laws in the lower house last week, and two abstained. At least two government senators planned to defy Howard in the senate, where the government has a one-seat majority.
Monday's developments coincided with the discovery of eight illegal immigrants on an island in the Timor Sea.
Amanda Vanstone, the immigration minister, said eight people had been found on Ashmore Reef. They will be taken by the Australian navy to Nauru, where any claims for asylum will be processed.
"There are eight unlawful arrivals on Ashmore Reef apparently dumped by people-smugglers," Vanstone said. "The arrival of these people confirms the need for strong border protection."
Ties between Indonesia and Australia were strained and Indonesia withdrew its ambassador in a temporary protest after Australia granted asylum to the Papuan asylum seekers, who had arrived by boat in January.
Australia has courted Indonesian support for its tough stand on asylum seekers and sees Indonesia as crucial in its efforts to stop people-smugglers sending crowded refugee boats to Australia.
Howard said on Sunday that the new laws were not crucial to Australia's close ties with its neighbour, but a day later said he did not know if Indonesia would be upset that the new laws were not passed.
Late on Monday, Indonesia expressed regret over Australia's failure to introduce the tougher asylum laws.
Australia sees Indonesia as key
to stopping people-smugglers
Desra Percaya, the Indonesian foreign ministry spokesman, said Jakarta had been notified by Australia about Howard's failure to push through the legislation.
"But if what was reported in the media is true, Indonesia deeply regrets the government of Australia's failure to legislate the policy on asylum seekers that was introduced earlier this year," Percaya said.
Jakarta believes that by granting asylum to the Papuans, Canberra was supporting a secessionist movement in Indonesia's restive eastern province.
Mandatory detention for illegal arrivals has been at the centre of Howard's past two election wins. Church and human-rights group have condemned the stance.
Dissenting government politicians were angry that the proposed immigration laws would mean children would have been detained in Nauru, despite a promise by Howard a year ago that children would no longer be kept in immigration detention.
However, Howard said asylum seekers who arrived by boat on outlying Australian islands would still be sent to Nauru for processing under existing laws.