Hamilton won his fourth title in Mexico past year after starting third and then having to fight back from last to ninth following an opening lap collision with Vettel, who had been on pole but lost out to Verstappen.
Hamilton is now just two titles away from Schumacher's record of seven championships and 20 wins away from the German's record of 91 grand prix victories.
"How am I going to be fitter?" It hasn't kicked in right now. I hope that this kicks in soon.
Reflecting on his season Hamilton added: "It has been the toughest year physically, mentally and personally with everything I'm committed to, but I have wonderful support".
Verstappen added that the run-down to Turn One was "crucial" as he stormed past his team-mate before making the corner ahead of Hamilton, and from then on he was composed and confident in the cockpit. Verstappen took a comfortable race win, while Vettel battled hard to take second. It is not over for me. Vettel said: "I think we got more or less everything out of the vehicle, but dropping to fourth from second is not satisfying". "We tried to make the best of it, I thought we had enough but it's still good to be second".
"For now I am not the happiest guy, but in two weeks' time I will step into the auto I always dreamed of driving and there is plenty to be happy about". I don't know if that's something that comes with age but I'm sure that helps. "I need him at his best to fight him again". My fans have been wonderful, my family have been so supportive, but most importantly Mercedes and my team, they have been the most incredible unit.
"We've got to finish the job tomorrow, but to confirm our pace in qualifying is really good". "I never felt that I was really put under pressure". Hamilton is on 71 victories; Schumacher won 91.
"I still wasn't convinced it was the cleanest lap, but I've got to relax a little?- I'm tripping major nut-sack right now", he said in his post-session interview after claiming his third career pole and first anywhere other than Monaco. "He is the best, or one of the best of this generation; he is exceptional", he said.
"Naturally I am gonna keep racing". How can I be a better all-round driver, not just in the auto but with my team in the garage, with the engineers and in the factory. "I hope you are having a great weekend and I hope the rest of 2018 is an unbelievable year for you".
That was the pre-recorded message from Hollywood legend Will Smith that was played to Hamilton on team radio as he cruised around on his cool down lap in Mexico City.