The Mercedes driver collided with the Ferrari of former teammate Lewis Hamilton and ended up spinning off into the gravel.
Russell had started in third place on the grid but dropped down to sixth after losing ground on the straight.
In fighting back, the Briton went side by side with Hamilton and the pair made contact. After spinning off, Russell stepped out and walked away as seven-time champion Hamilton continued, with the safety car deployed.
Stewards investigated and gave Hamilton a five-second penalty for causing a collision.
Formula One leader Kimi Antonelli, who is 25 points clear of his Mercedes teammate and closest rival in the standings after nine of the 22 rounds, had started on pole position chasing his sixth win of the season.
Russell, who has now failed to score in three races this season, while Antonelli has suffered two blanks, said he felt numb.
"When it happens so often, you just get used to it," he said.
"I made a great first corner and I was tucked up right behind (Red Bull's Max) Verstappen, but for whatever reason the battery decided not to recharge at Turn One," he explained.
"I exited the first corner 35% down because of that, and it didn’t charge, I had a boost problem, the turbo didn’t sort itself out, so no power, and I got to the top of Eau Rouge with 0% battery, and quite frankly it was dangerous.
"I got swamped by three cars, and I shouldn’t have been in that position in the first place, and that is why I am most angry. The incident with Lewis was a racing incident. He didn’t do it on purpose. He was more to blame than I, but he didn’t do anything reckless."
Russell said after qualifying on Saturday that there was a serious issue with his car on the straights.