Hamilton fell 19 points behind Max Verstappen following the Dutchman’s victory in Mexico.
Verstappen moved past both Hamilton and pole-sitter Bottas with a magnificent start at the Autodromo Hermanos Rodriguez before going on to score an impressive win.
Starting second, Hamilton’s reaction time might have been three thousandths of a second quicker than Verstappen’s, but Bottas allowed the Red Bull driver an opening when he left the racing line unguarded.
Verstappen hardly needed the invitation, jinking out of Bottas’ slipstream before out-braking both Mercedes drivers to seize the lead.
Hamilton has slipped from 12 to 19 points behind Verstappen with only 107 points on the table.
“I envisaged the start differently in the sense that Valtteri would get a better start and I would try to get into his tow,” said Hamilton.
“I was covering my side of the track and making sure that nobody could come up the inside and try to keep whichever Red Bull I could see in my mirror behind.
“I thought Valtteri would be doing the same, but obviously he left the door open for Max.
“Max was on the racing line and did an amazing job braking into turn one. I was on the inside and there was no opening.”
Hamilton’s Mercedes boss Toto Wolff concurred with his superstar driver.
“That shouldn’t have happened,” said the Austrian. “We had two cars in front and seemed to open up the sea for Max to come around the outside. It is annoying to say the least.”
Bottas, who will be replaced by British driver George Russell next season, spun at the second corner after tangling with McLaren’s Daniel Ricciardo. He finished 15th.
“It made my race a lot harder,” said Hamilton, who spent the closing stages of the race holding off Verstappen’s team-mate Sergio Perez.
“Having one Red Bull car ahead and one behind allows them to play the strategy. Sergio was super close and I couldn’t pull away from him. But when there is a will there is a way, and we managed to keep him behind.”
Despite his latest defeat, Hamilton has not given up hope of winning a record-breaking eighth title.
“There are still four races to go. Nineteen points is a lot of points and Max has nine wins and that is a lot of wins,” he said.
“If they were to carry their superior speed into the next races we may be in trouble, but I hope we will be closer.
“They have the faster car, but all I can do is try and squeeze everything out of our package, make sure we don’t leave any stone unturned, maximise what we have, and give it my all.”