At one stage, they almost crashed into the Italian quartet before Team GB finished fourth.
Cook admitted after the race took responsibility for the steering error before bursting into tears.
“I need to diagnose it but I feel I screwed up a bit and as I was closing in at the end and taking big strokes at the end going for the line I forgot the steering and that’s what cost us to be honest, cost us a medal,” he said.
“All I can say is thank you to everyone who stayed up to watch tonight and I’m really sorry we’re not coming back with something.
“I’m really proud of these guys to get us through this season. I had Covid at the beginning of the year and to get here was not a given.”