BP made an underlying profit of $3.2 billion in the three months to March, down $1bn on the same period last year.
The fall in profits partly reflects a $521-million write-off relating to the company's Utica shale acreage in Ohio.
"As a consequence of disappointing appraisal results, we have decided not to proceed with development plans in the Utica shale," said BP.
The reverse highlights the challenges some firms have faced trying to make some of their hefty investments in shale acreage pay.
The fall in profits also reflected a 8.5% drop in production compared with the first quarter of 2013. This was partly due to the sale of assets BP has offloaded since the serious spill on its acreage in the Gulf of Mexico in 2010.
However, BP noted: "With new major project volumes in the North Sea, Angola and the Gulf of Mexico, we have grown our total underlying production in higher-margin areas."
The comments refer to fields in Norway, but BP is investing heavily in new UK assets, like Clair Ridge off Shetland.
At its recent annual general meeting BP's chairman Carl-Henric Svanberg appeared more sanguine than Mr Dudley about the prospect of Scotland voting for independence in September.
Mr Svanberg told the meeting: "It would not have, I would say, any major implications long-term but anything that creates uncertainty will always mean more caution from business investors."
Mr Dudley told it: "We have a £10 billion programme of investment over the next 10 years in the North Sea. Therefore uncertainty does make us think carefully about issues like currency and other things."
In February he said his personal view is the United Kingdom should stay together.
BP's downstream profits slipped to $1bn in the first quarter from $1.6bn last time following a fall in refining margins.
Its share of profits at Russia's giant Rosneft fell by 75% to $271m in the fourth quarter, from $1.1bn in the previous three months.
The rouble plunged amid western powers' criticisms of Russia's actions in Ukraine.
BP acquired a near 20% percent stake in Rosneft in the first quarter of 2013.
America is imposing sanctions on Rosneft's chief executive, Igor Sechin, whom it links with Vladimir Putin. But Mr Dudley said BP is committed to its investment in Rosneft and plans to invest in Russia long term.
BP said there remains significant uncertainty about what the final costs of the Gulf of Mexico spill will be. These increased by $29m in the first quarter to $42.7bn.
Mr Dudley said BP has achieved "real business momentum" from its efforts to boost cash returns.
BP will pay a quarterly dividend of 9.75 cents per ordinary share, up from 9 cents last year. More share buy-backs are on the cards.
Analysts at Investec said BP had made a "solid start" to 2014.
Shares in BP closed up 3%, 14.25p, at 502.6p in London.