NEW ORLEANS — Transocean employees should have done more to detect signs of trouble before the company’s drilling rig exploded in the Gulf of Mexico in 2010, killing 11 workers and triggering the nation’s worst offshore oil spill, the company’s chief executive testified Tuesday.

But the Swiss-based drilling company’s own investigation of the disaster didn’t find any mistakes beyond the rig floor, Steven Newman said. He testified on the 14th day of a trial designed to determine the causes of BP’s well blowout and to assign fault to the companies involved.