On the Friday following the Albert Park race, the FIA issued a summons for Ferrari's Right of Review, a hearing which took place on Tuesday.
That determined whether significant, new, and relevant evidence existed.
The decision means the five-second penalty and Sainz's 12th place in the Australian Grand Prix stands.
“Very disappointed that the FIA did not grant us a right of review,” Sainz wrote on social media.
“Two weeks later, I still think the penalty is too disproportionate and I believe it should have at least been reviewed on the basis of the evidence and reasoning we have presented.
“We have to continue working together to improve certain things for the future.
“The consistency and decision making process has been a hot topic for many seasons now and we need to be clearer for the sake of our sport.
“What happened in Australia is now in the past and I am 100 percent focused on the next race in Baku.”
The outcome sees Sainz remain fifth in the drivers' championship with 20 points and Ferrari fourth in the constructors' standings with 26.
Formula 1 returns for Round 4, the Azerbaijan Grand Prix, on April 28-30.
You can read the decision of the stewards in full here.