Hamilton, who won his fourth Formula One championship two week ago in Mexico, walked away from the vehicle without appearing injured and will start at the back of the grid on Sunday.
"Even though he is a really, really good driver and very consistent, I also need to believe in myself. I tend to just look at it as challenges are what makes life interesting and overcoming them makes life meaningful", Hamilton told Sky Sports.
Daniel Ricciardo was fifth fastest but finished the session over 0.9s off Bottas' best time, while Red Bull teammate Max Verstappen spun on the exit of the final corner of his hot lap and finished ninth.
Hamilton, 32, sealed his fourth world title - and third in the past four seasons - on October 29 at the Mexico Grand Prix.
"I had a better run at the end of my out-lap, so there was probably more grip than I expected there".
"It was a shame that Lewis is out, a shame for us, but I stood up for the team and it is good to start from pole position here". It was just a nice lap.
Sergio Perez was sixth for Force India ahead of resurgent two-time champion Fernando Alonso of McLaren Honda, Nico Hulkenberg and his Renault team-mate Carlos Sainz. I chickened out a little bit with the brakes.