Bianchi (Marussia) collided with a recovery vehicle that was dealing with a similar incident involving Adrian Sutil (Sauber), which ultimately led to proceedings finishing on lap 46 on Sunday.
The Frenchman subsequently headed to hospital unconscious, leading Massa to suggest the start time should have been altered with inclement weather forecast - particularly towards the end of the day.
Asked whether it should have been run earlier, Williams' Massa said: "Yes, or maybe yesterday."
Those sentiments were echoed by Sutil, who added: "We were not asked our opinion on whether it should start earlier but I think it should have.
"It got more wet as the day went on and it would have been quite easy to make the race earlier."
Massa, who later headed to the hospital where Bianchi was being treated, also felt the safety car came out too late.
He said: "I am very worried that he (Bianchi) hit the truck. I thought the race finished too late.
"I was screaming five laps before the safety car that it was too wet. They waited too long. It was dangerous."
Lewis Hamilton won the race, edging out Mercedes' team-mate Nico Rosberg to extend his lead atop the Formula One drivers' standings to 10 points.