The 30-year-old was trapped LBW by ex-England seamer Ryan Sidebottom in the third over of the day, although did last longer than his former Test opening parter Nick Compton who departed first ball.
Cook’s innings was his first in the first-class format since being ditched as England’s one-day captain in December, just two months before the World Cup, in favour of Eoin Morgan.
The Essex opener has since suggested that England’s dismal World Cup performance, where they exited at the group stage having posted just two victories from six pool games, proved that decision to be misplaced.
Cook will lead England during their three-Test tour of the West Indies next month before a series against New Zealand precedes a home clash with Australia, which starts in June.
Despite being England’s leading centurion with 25 Test tons, a score of three will be viewed as an inauspicious start to an Ashes year for a player without a century in the longer form of the international game for 31 innings.