However the two leaders insisted that their countries must keep troops in Iraq and called on the international community to give its full support to the new Iraqi government.
The pair carefully avoided setting a timetable for the withdrawal of coalition troops from Iraq.
Mistakes
Mr Bush said his biggest regret of the war was the ongoing damage caused by the revelations of prisoner abuse at Abu Ghraib.
He said it was the "biggest mistake that's happened so far, at least from our country's involvement in Iraq ... We've been paying for that for a long period of time".
Mr Bush also admitted that his bellicose "bring 'em on" war cry to Iraqi insurgents in July 2003 was a big mistake, saying that kind of tough talk sent the wrong message.
"I learned some lessons about expressing myself maybe in a little more sophisticated manner, you know. 'Wanted, dead or alive', that kind of talk. I think in certain parts of the world it was misinterpreted," he said.
Mr Blair said the "de-Baathification" of Iraq -- efforts to rid Iraq's army of Saddam Hussein's followers -- had been badly handled.
"I think it's easy to go back over mistakes that we may have made. But the biggest reason why Iraq has been difficult is the determination by our opponents to defeat us. And I don't think we should be surprised at that," Mr Blair said.
Both Mr Bush and Mr Blair have seen their public standings collapse over the past year, in large part because of the war, but both insist they were right to order the March 2003 invasion.
The leaders remain close allies but there is widespread recognition that the Bush-Blair era is drawing to a close.
Mr Bush's second presidential term in office expires in 2008, and he is not permitted to stand again. Mr Blair has said he will not seek a new term and already faces calls to stand down.
There are around 135,000 US troops in Iraq and around 8,000 British troops.
More than 2,400 coalition soldiers and thousands of Iraqis have died in violence since the March 2002 invasion.
Admission
Both men said their support of the war in Iraq had led to considerable disquiet in their countries.
"No question that the Iraq war has created a sense of consternation here in America," said Mr Bush.
"I mean, when you turn on your TV screens and see innocent people die day in and day out, it affects the mentality of our country."
"Not everything since liberation has turned out as the way we had expected or hoped. We've learned from our mistakes, adjusted our methods and have built on our successes," said the US president.
"The decision to remove Saddam Hussein from power was controversial. We did not find the weapons of mass destruction that we all believed were there, and that's raised questions about whether the sacrifice in Iraq has been worth it," Mr Bush said.
"Despite setbacks and missteps, I strongly believe we did and are doing the right thing," he added.
Call for support
Mr Blair expressed optimism after his visit to Baghdad on Monday to meet new Prime Minister Nouri al-Maliki, saying he believes it may be possible for Iraqi forces to take over nearly all security duties by the end of 2007.
"Inevitably, over time, we have to transfer responsibility" because it will be easier for an Iraqi interior minister "who is the product of an Iraqi-elected government to go in and take the really tough measures sometimes that is necessary to sort some of these issues out," he said.
But for now: "This directly elected Iraqi government has said they want us to stay until the job is done," he added.
Both leaders acknowledged the decision to invade Iraq in 2003 had been divisive, but agreed it was time to look to the future now that the Iraqis had gone to the polls and freely elected a new government.
"It is our duty, but it is also the duty of the whole international community to get behind this government and support it," Mr Blair said.