The clash occurred as both the Toro Rosso and Caterham pitted on lap seven.
Vergne was released from his pit as Pic was pulling in ahead of him.
The cars came together, breaking the Toro Rosso's front wing and leaving Pic skewed sideways across the Caterham pit stall.
The stewards ruled that Toro Rosso's pit release had been unsafe and imposed a $10,000 fine.
Team boss Franz Tost said: "We agree with their decision."
Both drivers continued, with Vergne getting back to 10th and Pic finishing 14th.
Vergne felt the incident cost him a much better finish.
"It's a shame that a mistake in the pits cost us so much, as I could have done something better," he said.
"So, overall I feel rather frustrated. But I'll take the point gladly."
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- Toro Rosso