Brown, expected to take over as premier when Blair steps down this year, said: "Now that we know the full picture of what happened, we can sum this up as a deplorable set of events."
A mobile phone video showed observers taunting Saddam with shouts of "go to hell" and chanting the name of a Shiite cleric before the former Iraqi leader fell through a gallows trapdoor.
The images provoked international criticism and further inflamed sectarian passions in Iraq. Iraqi Prime Minister Nuri al-Maliki has pledged to investigate the way the hanging was conducted.
Asked about the hanging when visiting a London hospital on Friday, Blair said: "I've decided to talk about health today. I will talk about all those other issues next week."
Blair was on holiday at the Miami home of pop star Robin Gibb of the Bee Gees when the execution took place.
President Bush has said Saddam's hanging should have been carried out in a "more dignified way" but argued that he received justice, unlike his victims.
Gordon Brown, laying out his stall as a future prime minister in a BBC TV interview to be broadcast on Sunday, said:
"Even those people, unlike me, who are in favor of capital punishment found this completely unacceptable. It has done nothing to lessen tensions between the Shia and Sunni communities."
Brown flew to Iraq in November to visit British troops stationed in the south of the country.
He faces a tough challenge stepping into Blair's shoes. The Labour government has been undermined by the war in Iraq and is beset by scandals, while the opposition Conservatives have revived their fortunes under youthful leader David Cameron.