"I didn't feel anything," he said, adding that he had been getting rid of bodies for about 10 years.
"May they forgive me," he said, surrounded by armed soldiers.
Most of the bodies dissolved in about 24 hours, with the remains then buried in a nearby pit, Meza, 45, said.
'Telling the truth'
A high-ranking officer in the army said he believed that Meza, who was arrested with three other people on Thursday, was telling the truth.
Those killed are believed to be rivals of Teodoro Garcia Simental, an alleged former lieutenant of the Arellano Felix drug gang, authorities said.
Police in Tijuana have in the past recovered human remains burned with acid in and around the city.
The drug war claimed 5,700 lives across Mexico last year, more than double the number of victims in 2007, while scores of other people have been abducted by gangs.
Felipe Calderon, Mexico’s president, has deployed thousands of troops across the country in an attempt to crack down on the cartels.