Brazil had led 2-0 going in to the half-time interval after goals from Leandro Goncalves do Amaral and Maycon Ferreira de Almeida, but David Porcher helped Britain to hit back with an impressive strike just three minutes after the break.
Crossen, 26, who suffered a stroke just three years ago, had a couple of frustrating moments throughout, but looked to be on good form with several shots on target. In the final moments, it looked as though Crossen could score the equaliser, only for the ball to fly over the cross bar.
Crossen formed part of the 2015 Cerebral Palsy World Championship team who secured qualification for these games with a 5th place.
Despite the national Football Associations blocking British teams from participating at the Olympic Games, football at the Paralympics has enjoyed a wealth of support, including a good luck message from England captain Wayne Rooney.
The preliminaries were always going to be a challenge for the British side, who not only have Brazil for company in a tough Pool A, but also Ireland and Paralympic champions Ukraine.
Great Britain will face Ukraine on Saturday 10th September (14.00 BST).