The former champions had sought a review of five incidents at the April 29 Azerbaijan Grand Prix, arguing that significant and relevant new elements had emerged.
The stewards unanimously rejected that, however.
Sirotkin had crashed into the back of the Force India driven by Mexican Sergio Perez, who ultimately finished third in a chaotic race in Baku, on the opening lap with the Russian retiring immediately.
The stewards said the incident "was not similar to other first lap incidents where cars were side-by-side. The penalty was similar to other penalties for similar collisions and was consistent with the minimum grid penalties given previously."
Williams had questioned the stewards' decision in relation to other collisions.
They had also referenced the response to McLaren's Fernando Alonso, who was hit on the first lap and limped back to the pits with two punctures before rejoining with a badly-damaged car and finishing seventh.
That was one place ahead of Williams' Canadian teenager Lance Stroll.
Race director Charlie Whiting, who was present in the meeting convened by teleconference, noted that Alonso returned to the pits while the Safety Car was deployed.
He had also taken care to avoid the racing line and keep clear of following traffic.
The stewards said Williams were well aware of what was going on at the time.
"The team on the pit wall would have seen the driver of car 14 (Alonso) enter the pits, as it had to drive past them. Therefore it cannot be argued that this is a 'new element'," they declared.
Williams had also argued that a 10 second penalty imposed on Haas driver Kevin Magnussen for a collision with Toro Rosso's Pierre Gasly was 'inconsequential'.
Stewards reminded the team that, since 2013, the consequences of penalties were not taken into account.
"In relation to other penalties, since the beginning of 2016 there have been a total of 87 incidents involving alleged 'causing a collision' in the Formula One Championship," the statement noted.
"Of these, as a result of the 'let them race' policy, 55 have resulted in No Further Action. Fourteen have resulted in 10 second penalties and nine have resulted in three grid position penalties for the next race.
"Therefore the penalties imposed...were entirely consistent with previous practice and with the penalty guidelines."
(Reporting by Alan Baldwin, editing by Ed Osmond)
