"Iran is interfering quite heavily and this is worrying," he said.
He accused the Iranian government of interfering by inviting all the major parties to Tehran for talks, except his own Iraqiyya bloc.
"They have invited everybody - but they haven't invited us - to Tehran," he said.
He said he was concerned Tehran was also influencing a commission that has been vetting candidates for ties to Saddam Hussein's Baath party, which may disqualify more of his supporters.
Some are likely to see Mr Allawi's comments as an excuse for the possibility he may not be able to form a government, says our correspondent.
While many Shias backed him, others are suspicious of his past links to the Baath party.
The Iranian embassy in Baghdad declined to comment.
According to final results published by Iraq's Independent High Electoral Commission (IHEC), Mr Allawi's secular Iraqiyya bloc won 91 of the Council of Representative's 325 seats, 72 short of a majority.
Al-Iraqiyya (Iraqi National Movement): Nationalist bloc led by former PM Iyad Allawi, a secular Shia. Includes Vice-President Tariq al-Hashemi, a Sunni Arab, and senior Sunni politician Saleh al-Mutlaq
State of Law: Led by Prime Minister Nouri Maliki and his Shia Islamist Daawa Party, the alliance purportedly cuts across religious and tribal lines. Includes some Sunni tribal leaders, Shia Kurds, Christians and independents
Iraqi National Alliance (INA): Shia-led bloc includes followers of the radical cleric, Muqtada al-Sadr, the Supreme Iraqi Islamic Council (SIIC), and the Fadhilah Party, along with ex-PM Ibrahim Jaafari and Ahmad Chalabi
Kurdish alliance: Coalition dominated by the two parties administering Iraq's semi-autonomous Kurdish region - the Kurdistan Democratic Party (KDP) and Patriotic Union of Kurdistan (PUK), led by President Jalal Talabani
Mr Maliki's State of Law came second with 89 seats, followed by the Iraqi National Alliance (INA) on 70, and the Kurdistan Alliance with 43.
Iraqiyya's narrow victory means Mr Allawi, a Shia, will be given the first opportunity to form a coalition government.
If he fails to do so within 30 days, Iraq's president will ask the leader of another bloc.
There is concern that a challenge to the election result could be lengthy and divisive, endangering progress towards greater stability.
Sectarian violence erupted in 2005 as politicians took months to form a government after the last parliamentary election.
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