In an interview on US TV, Mr Karzai said the resignation of an Afghan member of the UN-backed panel "cast serious doubt" on its work.
Mr Karzai said that fraud was likely to have taken place in the August vote, but called it "good and fair".
He leads the preliminary count but the panel's findings - due imminently - could force the vote to a second round.
The election has been mired in controversy since it was held in August, with accusations that fraud was committed on a huge scale.
The interview came a day after Mustafa Barakzai quit the UN-backed Electoral Complaints Commission (ECC), which is investigating irregularities.
The panel is due to rule in the next week on the outcome of its findings.
"I am not going to say the Electoral Complaints Commission is illegitimate," Mr Karzai told ABC network's Good Morning America.
But he added: "That resignation has cast serious doubt on the functioning of the commission.
"I hope it should do everything now to remove those suspicions and to remove any other stigmas and to prove it is impartial and fair and not dictated to by foreign elements and government," he said. Mr Barakzai, a Supreme Court judge, had alleged that foreigners were "interfering" in the panel's work and Afghans had little input in its key decisions. He was one of two Afghans on the five-member UN commission.
A deputy campaign manager for Abdullah Abdullah said the resignation was politically motivated.
"Barakzai's resignation has a direct connection to Karzai. It was Karzai's idea," Saleh Mohammad Registani told the Associated Press news agency.
"Karzai is trying to bring the work of the ECC into question."
'Worthy of praise'
Mr Karzai conceded that some irregularities must have taken place but insisted that the elections were a success. "There were irregularities, there must have also have been fraud committed," he said.
"But the election was good and fair and worthy of praise not of scorn which the election received from the international media, which makes me unhappy, which makes me angry," he said.
He warned: "We must not turn an election, a victory for Afghan people, into a nightmare for the Afghan people."
Mr Karzai also said that he was "fully behind" new Nato commander Gen Stanley McChrystal and his emphasis on protecting Afghan civilians.
A recount of a sample of suspect ballots is almost complete, the UN said on Sunday. About 10% of votes cast in August are being audited.
But on Monday the ECC once again altered its formula for counting the contested votes.
Mr Karzai leads preliminary results with about 55% of the vote, considerably ahead of former foreign minister Dr Abdullah, who has 28%.
There would be a second round run-off if neither secures 50% of ballots cast.
In an interview with Reuters on Monday, Dr Abdullah softened his stance on the outcome of the elections adding that he would be amenable to a place in a unity government.
In Tuesday's interview, Mr Karzai said that for the past seven years, he had been known as "a man who brings inclusiveness".
"The unity of [the] Afghan people is paramount here and we will continue to strive for that," he said.