The pair banged wheels as they fought over sixth place, causing Massa to sustain a puncture and go off-track at turn 15.
After an investigation by the stewards, it was deemed that "no driver was wholly or predominately to blame for the collision"
However, Massa was adamant that Alonso was at fault, telling Sky Sports: " for sure, his responsibility."
"I was just doing the corner and he just dived completely inside," the Brazilian said. "I was already entering the corner and he just hit my car and I had a puncture. It just destroyed my opportunities I had on that moment."
Alonso, meanwhile, had other ideas.
"I think that I was side-by-side with him," he said. "It's not that I was coming from behind or any crazy thing, there was not the space to turn in, but the stewards will decide. Hopefully it remains as a race incident."
The result meant that Alonso moved ahead of Massa into 10th in the drivers' standings.
Bahrain International Circuit - Winter testing