The two were battling for third place, with Perez hoping even to grab second at a favourite circuit when they made contact at turn two and ended up in the wall.
"It's a disaster for the championship," said Perez, who has not been on the podium since China in April and leaves Baku eighth overall and 170 points behind team mate Max Verstappen.
"In my opinion, Carlos moved too quickly to follow the tow from Charles," added the Mexican, who had tried to pass Ferrari's Charles Leclerc for second but dropped to fourth as Sainz went past.
"It was just wrong time, wrong moment and it resulted in a huge shunt."
Sainz told reporters after seeing the stewards that he was glad the two were unhurt and refused to shoulder the blame for what he called an unexpected contact.
"I didn't do any erratic manoeuvres, any aggressive moving on Checo (Perez) or anything like that, and for some reason that I don't understand still, we collided and that was the end," he said.
"I'm 100% convinced I didn't do anything wrong or anything aggressive."
Red Bull team boss Christian Horner said Perez deserved a lot more.
"I was just looking at the replay and you can see Carlos start to drift across the circuit, so very very disappointing," he added. "He (Perez) should at the very least have been on the podium today.
"It's destroyed the race for Checo today. It's cost us a lot of damage and obviously vital points in the constructors' championship."
Red Bull fell 20 points behind McLaren, who won with Australian Oscar Piastri, with seven grands prix and three sprints remaining. It was the first time since early 2022 that Red Bull had not led the championship.
Sainz and Perez had clashed previously over the weekend, each visiting the stewards for impeding the other in practice.
Perez collected a warning for impeding Sainz on Saturday and Sainz the same for holding up the Mexican on Friday.
"I think it's the third time. Now they've finished the job," commented Piastri as he watched a replay of the collision in the cool-down room.
