"Such a government which lacks legitimacy cannot fight corruption," he told reporters.
"A government which comes to power without the people's support cannot fight the phenomena of terrorism threats, unemployment, poverty and hundreds of other problems."
Dr Abdullah said the election commission, which critics say was biased towards Mr Karzai, had exceeded its mandate. Other critics have called Mr Karzai's victory unconstitutional because he did not secure more than half of the vote.
BBC correspondents say it is difficult to assess the motives for Dr Abdullah's remarks at this point, or whether they might be seen as a call to action by his supporters.
The former foreign minister has urged those who back him to remain peaceful. He again called on his supporters to show restraint and not do anything illegal to oppose the government.
Mr Karzai has promised his new administration will be inclusive, but Dr Abdullah ruled out playing any role - despite pressure for a unity government.
"I have no interest in the future cabinet of Karzai's government and I will pursue my agenda, which is change," he told the news conference at his Kabul home.
But he said he would not challenge Mr Karzai's re-election.
"The process has completed itself with that final, illegal decision," he said. "I leave it to the people of Afghanistan to judge."
'Puppet'
Dr Abdullah's comments came a day after Mr Karzai vowed to remove the "stigma" of corruption and held out the prospect of talks with "Taliban brothers".
Hamid Karzai's administration has been accused of corruption
The Taliban responded by saying they would continue their fight and called Mr Karzai "a puppet".
On Monday, poll officials scrapped a run-off vote that had been planned for this weekend.
Mr Karzai agreed to the run-off after hundreds of thousands of votes were discounted from the 20 August first round because of widespread fraud.
After an investigation by the UN-backed Electoral Complaints Commission (ECC), Mr Karzai's share of the vote dropped to 49.67% - below the crucial 50% plus one vote threshold needed to avoid a run-off.
The crisis has paralysed the Afghan government for months, and delayed decisions by the US and other Nato partners on sending more troops to combat the insurgency.
Bookmark with:
What are these?