"We are going to hold ourselves to a higher standard. I suspect that the American people and the regulators in the United States will hold us to a higher standard. That seems reasonable to me and we are going to respond to that and we are going to change," Dudeley said in an interview with ABC News.
"I think sometimes events like this shake you to the core, the foundation, and you have two responses: one is to runaway and hide; the other is to respond and really change the culture of the company and make sure all the checks and balances are there, just to make sure this does not happen again."
The company said it would consider its position on future dividend payments at the time of its fourth-quarter results.
Analysts had expected BP to set aside tens of billions of dollars to cover the cost of the April 20 oil rig explosion that killed 11 people, ruined the Gulf's fishing and tourism industries, and polluted the Gulf shoreline with slimy goo.
Dudley said the accident that lead to the oil spill "came out of nowhere", and dismissed the company's safety record as outdated.
"Many of those accidents occurred about a half-a-decade ago and that's what you see rolling through in terms of those safety violations,” Dudley said.
"When Tony Hayward did come in he laid the foundations for a strong focus on safe and reliable operations and the company has been moving in that direction, it takes some time."
After BP's announcement of a replacement, Hayward said: "I believe that it is not possible for the company to move on in the United States with me remaining as the face to BP.
"So I think that for the good of BP, and particularly for the good of BP in the United States, it is right for me to ... step down."
Hayward is reportedly leaving with a total pay-off and pension package worth around $18.5m, and will be appointed as a non-executive director at TNK-BP as part of his departure deal.
He became a controversial figure due to his handling of the environment crisis that developed after after an explosion in April that killed 11 workers and caused the Deepwater Horizon rig to sink.
The destroyed wellhead in the Gulf of Mexico seabed gushed millions of barrels of oil into the waters off the southern US coast.
Public relations gaffes
BP capped the leaking well last week after a series of failed attempts to stem the leak over the last three months.
Hayward has been criticised for a string of public relations gaffes during the crisis, at one point included telling reporters "I want my life back".
||$32.2 billion set aside for cleanup costs
||BP plans to sell $30bn in assets over next 18 months
||$16.97bn lost in second-quarter earnings
||Company stock down 37.7% over last three months
BP said that it "will be a different company going forward, requiring fresh leadership", but defended the outgoing chief's performance.
"The BP board is deeply saddened to lose a CEO whose success over some three years in driving the performance of the company was so widely and deservedly admired," BP Chairman Carl-Henric Svanberg said in a statement.
Dave Kansas, the Wall Street Journal's European markets editor in London, told Al Jazeera that Dudley had been favourite for the post of chief executive because of his handling of the clean-up.
"He [Dudley] grew up on the Gulf coast in Mississippi ... he's received high praise from some of the government officials around the BP situation," he said.
"The PR piece of this looks like it's probably sliding into a place that BP would like."
He said that having an American take the chief executive slot was also important for the company given the widespread criticism it has faced from politicians and the public across the US.
Despite the steep costs of cleaning up the massive oil spill and the expected government fines, BP has sought to reassure investors that it continues to remain a strong company.
|BP has earlier promised $20bn to pay the claims of those affected by the spill [AFP]
David Strahan, an energy analyst and author of the book The Last Oil Shock, backed up those assertions.
"There's no way this company's going to go bust as a result of this, despite the eyewatering size of the numbers," he told Al Jazeera.
But he said the amount BP has set aside to cover costs may not be large enough.
"I'm not sure that they have yet set aside enough to cover all of their liabilities, although I don't doubt that they could fund them, even if their numbers go up," he said.
Of the $32bn set aside, $20bn has already been pledged to payout claims made by those affected by the spill. The company's has also spent around $4bn of that money containing the disaster, leaving only $8bn for fines and other costs.
The news of Hayward's departure followed a weekend announcement that BP would finish installing the last bit of pipe into a relief well engineered to help permanently plug its oil spill in the Gulf of Mexico in the coming week.
Once the pipe is cemented in place, BP is supposed to begin a "static kill" sealing process in the first week of August.
The operation aims to seal the well by pumping heavy drilling mud through the blowout preventer valve system that sits on top of the well and then injecting cement inside to seal it.