Vettel, who finished first in Montreal on June 9 but was demoted to runner-up behind Mercedes' Lewis Hamilton after a five second penalty, told BBC radio he was disappointed with the outcome.
Ferrari team boss Mattia Binotto, who had sought a review of the Montreal decision, echoed the sentiment and told reporters the matter was now closed.
"As Ferrari we are all very unhappy and disappointed. We are disappointed certainly for Ferrari but for the fans and for our sport," he said.
The Italian team believed they had 'overwhelming' proof to trigger a review but the FIA revealed some of that was Sky Sports' television analysis carried out by Indian racer Karun Chandhok.
The Indian, who raced in Formula One for now-defunct tail-end teams Hispania and Team Lotus in 2010 and 2011 without scoring a point, was apparently unaware that his opinion formed part of the evidence.
"Er... so, can I send you an invoice Ferrari? I mean, lawyers send bills whether you win or lose a case so...!!," he said on Twitter.
The stewards decided Chandhok's video was "new but not significant and relevant" and the "personal opinion by a third party".
The ruling means that Hamilton, a five-times world champion, has his 29-point lead over team mate Valtteri Bottas confirmed.
Mercedes have won all seven races this season, and nine in a row in total, and are favourites to chalk up another in France on Sunday.
Ferrari sporting director Laurent Mekies had said earlier that the team believed the evidence to be "quite overwhelming when it comes to establishing that Sebastian did not breach any regulations."
The stewards clearly found it underwhelming.
They said footage of Vettel's face camera was previously available, as were analysis of telemetry data, camera angles from the car, post-race video images and the German's witness statement.
The right of review calls for a team to present significant and relevant new evidence that was not available at the time of the decision. The stewards, whose ruling is final, had sole discretion to determine whether such a new element exists.
The controversy triggered by the penalty, for going off track and returning in an unsafe manner while defending the lead from Hamilton, is unlikely to die down in a hurry.
Drivers and former champions have taken positions on either side of the divide, with some suggesting the rules might need changing.
"There is a rule that I don't think should be there, which is a bit too drastic and a bit too black and white and doesn't interpret well the rules of racing, that is race hard and enjoy," said McLaren's Carlos Sainz.
(Reporting by Alan Baldwin, editing by Pritha Sarkar and Christian Radnedge)
