"It basically says to people, look, you conducted a trial and gave Saddam justice that he didn't give to others," he said.
"But when it came to execute him, it looked like it was kind of a revenge killing ... It just goes to show that this is a government that has still got some maturation to do."
Bush's comments came as the US secretary of state, Condoleezza Rice, admitted that the president's plan for a military build-up in Iraq would be unlikely to halt the violence there.
"Violent people will always be able to kill innocent people and so, even with the new security plan ... there is still going to be violence," Rice said in Kuwait whilst on a trip to the region to shore up support for the proposal.
The US plans to send 20,000 extra troops to Iraq in an attempt to halt the bloody cycle of sectarian conflict.
At least 65 people were killed in two blasts at al-Mustansiriya University in Baghdad on Tuesday whilst 45 others were killed in other attacks around the Iraqi capital.
A video of Shia officials taunting Saddam on the gallows has further inflamed sectarian tensions among Iraqis and drew international criticism.
"Bush's strategy has failed totally in Iraq and USA has already lost the war. The new plan will not work; it will only bring more deaths and make things in Iraq worse..."
Dimos, Hania-Crete, Greece
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Controversy flared again following the execution on Monday of Saddam's half-brother, Barzan Ibrahim al-Tikriti, who was decapitated by the noose.
Bush said the way Saddam's hanging was carried out reinforced doubts about the government of the Iraqi prime minister, Nuri al-Maliki, and made it harder for him to make the case to the American people to continue supporting it.
"I expressed my disappointment to Prime Minister Maliki when I talked to him the other day," Bush said.
While expressing no regrets that Saddam had been put to death, Bush had said previously the execution should have been carried out in a "more dignified way", and welcomed Maliki's promise of a full investigation.