The Italian Ducati rider won the season-ending Barcelona race but the Spanish Ducati Pramac rider came third, beating Bagnaia by 10 points in the final standings.
Martin, who will ride for Aprilia next year, would have had to finish ninth and Bagnaia first for the Turin-born 27-year-old to keep the crown.
Bagnaia won 11 MotoGPs and seven Sprint races this year.
Martin, 26, who has won his first title, said “it was tough to ride at the end because I was crying”.
In the interviews immediately after the race, Bagnaia said “I don’t want to take the spotlight away from him, he deserves that number 1”.
“Jorge made the difference; I didn’t see the point of taking the spotlight on his day of celebration.
“However, the awareness of having been the strongest of the season remains, but I paid for too many zeros, due to my mistakes,” he said.
“But if you lose in the right way, there is nothing dishonourable in defeat.
“Regrets? I’ve always paid attention to the feeling on the bike and in the first part of the season I underestimated this, I regret not having insisted a bit more in this aspect.
“Then there was the retirement due to a technical problem and three mistakes of mine, the most avoidable at Silverstone, because I pushed too much and it wasn’t necessary.”
The race was moved to Barcelona from Valencia after the deadly floods there.
ANSA