Almost 60 per cent of shareholders rejected the remuneration report, which awarded Dudley a USD 19.6 million pay package even though the company experienced a drop in profit and planned thousands of job cuts worldwide.
But the vote was only advisory, and merely registered displeasure.
The company said it got the message and promised to review its remuneration policy ahead of next year's meeting. New proposals are expected to be put forward for shareholder approval in 2017.
"We will sit down with our largest shareholders to make sure we understand their concerns and return to seek your support for a renewed policy."
Aberdeen Asset Management, which manages more than 290 billion pounds (USD 411 billion), was among those complaining BP's award system was too complex.
A representative from the Church of England also questioned the morality of such a rise, given that Britain is undergoing a time of fiscal austerity.
Shares in BP fell almost 14 per cent in 2015. Its earnings plunged 91 per cent in the fourth quarter, though much of that can be attributed to falling global oil prices.
The company also has been paying off costs related to the 2010 Deepwater Horizon disaster in the Gulf of Mexico, which is still weighing on earnings.
Underlying replacement cost profit, an industry standard to measure earnings, fell to USD 196 million from USD 2.2 billion in the same quarter a year earlier.
Ann Dowling, a non-executive director of BP, stressed in remarks ahead of the vote that the existing pay policy had been based on "true underlying performance how Bob and the team manage the aspects of the business over which they have control strategy, operations and safety."
