Rosberg will start ahead of his Mercedes teammate and championship rival at the front of the grid in Austin, and Hamilton has admitted that his own brake issues meant that the German was simply "too quick".
"Nico did a great job, I really struggled with my braking, the left-front brake was always cooler than the right-front brake and it kept catching," Hamilton told Sky Sports News. "That's where I was losing time but even if that wasn't the case then Nico was perhaps too quick today.
"It wasn't the easiest of sessions. Once you lose your confidence on the brakes because you know it is going to lock then you are kind of stuffed. I tried to improve but ultimately I couldn't get close to Nico."
Rosberg trails Hamilton by 17 points in the drivers' standings ahead of Sunday's race.