Polesitter Bottas and Hamilton had locked out the front row for Mercedes, with the team hoping to use that opportunity to exert control on the Mexico City race early on.
The two were three-wide heading into the first corner with Verstappen, who swept around the outside and claimed the lead of the race with Hamilton in pursuit - while Bottas was left facing the opposite direction after contact with a late-braking Daniel Ricciardo precipitated a spin.
Hamilton said after the race that he was trying to protect his side of the circuit, but felt that Bottas had not demonstrated the same tactic at the start.
"I had envisaged it differently, naturally, in the sense that maybe Valtteri had got a better start and I would have tried to get into his tow," Hamilton explained.
"But I was alongside him which was good, and then I was just covering my side of the track trying to make sure that no-one could come up the inside.
"So I was trying to keep whichever Red Bull I could see in my mirror behind, and I thought Valtteri would be doing the same.
"But obviously, he left the door open for Max, and Max was on the racing line so did a mega job braking into Turn 1.
"Because I was on the inside on the dirt, there was no hope for me."
Mercedes team principal Toto Wolff said that he could understand Bottas' position owing to the lack of vision from the mirrors, but felt that his two cars could have warded off an immediate threat from Verstappen at the start.
Verstappen was able to maintain the lead during the following safety-car period, produced by the incident involving Mick Schumacher and Yuki Tsunoda, who had both ended up pincering Esteban Ocon at Turn 2.
"These cars are very difficult to judge from the mirrors, what is actually happening behind you." Wolff said.
"But I think if they would have been more to the left he wouldn't have passed, he would have been blocked."
Bottas explained his misfortune at the first corner, which later snowballed into a miserable race at the Autodromo Hermanos Rodriguez in which he was stuck behind Ricciardo for the majority of the race, during which a slow pitstop ended his hopes of netting any consolatory points.
"The start was OK, not too bad, but Verstappen got a bit of a tow and he braked really late." Bottas told Sky F1.
"But then suddenly at the apex at Turn 1 I think Daniel hit me in the rear and right there I spun I couldn’t do anything and then after that the race was tricky to make progress.
"I was too close to cars and managing engine and brakes so I could manage it until I was getting too close then it was not easy."
Additional reporting by Luke Smith
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