Speaking at Egypt's Economic Development Conference in the resort town of Sharm el-Sheikh, Dudley said that oil prices - which have fallen around 60 percent since last June - had been a "huge shock" for companies like his.
The industry had been enjoying a world of luxury over the last few years, he said, when prices were above $100 a barrel.
"We're back into the normal world of volatility for oil and gas prices," he said on a CNBC-hosted panel. "Anything that happens that fast can have unintended consequences."
BP was the first European major to sound the alarm on tumbling oil prices - on December 10, it warned that it was implementing a cost-cutting program as a result.
In December, oil majors in Europe also received a stark warning from credit ratings agency Standard & Poor's (S&P), which placed BP, Total and Shell on a negative watch. It means the three firms are more likely to have their debt rating downgraded over the next three months.
In January, BP announced job cuts in its onshore operations in the U.K. It told CNBC that it expected a reduction of around 200 staff and 100 contractor roles in light of "major reshaping" for the business and "toughening market conditions."
Speaking on the same panel in Egypt, Philippe Boisseau, president of marketing and services at Total, said the price of oil was going to stay where it is.
He added that speculators were trying to bet where the price will be in the future, but stressed that nobody had the answer.
"We have both lower demand...and also we have global oversupply," Boisseau said.
Speaking at the investment event in Egypt, Dudley added that BP had operated continuously in the country for the last 25 years.
His comments come after the oil giant signed an deal to develop gas resources in Egypt, with investment of around $12 billion from BP and its partners. The company said the project underlined its commitment to the Egyptian market and was a vote of confidence in the country's investment climate and economic potential.
Three days later, BP also announced a gas discovery in the East Nile Delta which it said was expected to be the deepest well ever drilled in Egypt.
"I think the time is absolutely right," Dudley said about investing in the Middle Eastern nation.
"(Egypt) really is the lynchpin...it's the largest market in the Middle East."
On Saturday, Dudley said the investments would increase in gas production in the country by 25 to 30 percent.