Ben van Beurden said the Anglo-Dutch company was disappointed with its record in the North Sea last year, when it was plagued by a series of unplanned interruptions to production.
With the company's chief financial officer, Simon Henry, highlighting the cost of running ageing assets off Scotland, the directors' comments may increase the likelihood Shell could sell some North Sea interests.
Mr van Beurden, who took charge in January, stressed he saw scope to boost returns at Shell.
The pay of his predecessor, Peter Voser, halved to $11.24 million (£6.7m) last year following what the company described as a disappointing performance.
Shell suspended its controversial Arctic drilling programme earlier this year and pledged to cut spending and streamline operations following disappointing earnings in the fourth quarter of 2013, the least profitable for five years.
Mr van Beurden highlighted concerns about the performance of parts of the business in North America, where Shell has struggled to make hefty investment in shale resources pay. He signalled he would keep the North Sea under close scrutiny.
"We have to be honest with ourselves that the North Sea has disappointed for Shell in 2013," the Dutch executive said.
He added: "We need to figure out a credible and affordable plan to arrest decline in the North Sea."
Mr van Beurden noted high levels of maintenance down-time on North Sea assets cost Shell 15,000 barrels of production per day last year.
Mr Henry said Shell's North Sea assets were only available on average 50% of the time in 2013, compared with an industry average of 60%.
"We have some mature assets in the Central North Sea, Northern North Sea, that are the assets that are basically seeing lower availability," he added.
"Quite a few of these assets are at the margin as costs increase and the remaining resource decreases." Mr Henry said Shell would have to decide which assets to invest in and which might attract more resources from other owners.
Shell put three North Sea assets up for sale last month.
It operates 23 facilities in the Central and Northern North Sea, including eight platforms and three floating production storage and offloading vessels. But Mr Henry also underlined the company's enthusiasm for the West of Shetland area. It is investing in giant projects like Clair Ridge that could be producing for years.
"We have gas assets which typically are running well," he added.
Asked about competing claims about who is the best guardian of the North Sea made by the Westminster and Scottish Governments, Mr van Beurden said: "It would be better if Scotland stayed in the UK from a stability and predictability perspective.
"We are a company like many others that have investment horizons for many, many, years, decades.
"We are quite used to dealing with uncertainty ... but if we had a choice we would much rather have stability and predictability for many years to come."
Mr van Beurden wants the UK to remain in the EU.
Noting he had made similar remarks at a staff reception earlier this month, he concluded: "I would like to leave it at that."
"The business performance in 2013 was disappointing. This is reflected in the reward outcomes for the year," Shell's head of remuneration committee Hans Wijers said.
Mr van Beurden will receive a base salary of 1.4 million euros (£1.2m), compared with Mr Voser's 1.64 million euros.
The company will cut spending in its American exploration and production business by a fifth and could sell more of its shale assets.
Shell stuck to its 2014-15 divestment target of $15bn. Last month, Shell announced plans to offload stakes in a FPSO and a production platform off Scotland and a platform off Suffolk.
Royal Dutch Shell A shares closed down 26p at £21.505 in London.
Separately, GDF SUEZ said it has started full production from the Juliet gas field off Lincolnshire, at around 400,000 barrels oil equivalent a month.