He said he drove the car in one direction to test it, but then asked Thurman to drive it the other way.
He said he didn't realise there was a twist in the road coming back. Thurman posted footage of her crash on Monday.
The director said failing to test the route one more time was "one of my most horrendous mistakes".
Thurman suffered neck and knee injuries in the accident.
In a New York Times interview published over the weekend, Thurman said she had worries about the state of the car, but that Tarantino had persuaded her to go ahead with the scene.