Alonso received a 10-second penalty in China's sprint race after making glancing contact with Ferrari driver Carlos Sainz, which Alonso couldn't serve as he retired with a puncture.
Alonso, who also received three penalty points, said he didn't understand why he was penalised for what he felt was a racing incident.
Last week, Aston decided to ask for a right of review, which involves bringing significant, relevant and new evidence to the table to be judged by the stewards on Friday morning in Miami.
In the hearing, which was attended by both Aston Martin and Ferrari, the stewards disagreed that Aston's evidence cleared that three-pronged set of criteria, and therefore the matter won't be reopened further.
Aston provided forward-facing camera footage of the incident from Alonso's car, which was unavailable to the stewards when they made a snap decision during the sprint.
But while the stewards accepted the new footage was clearly new evidence and relevant to the incident, they felt it wasn't significant as they had enough alternative footage available at the time to make a decision, and the new camera angles wouldn't have changed their decision making.
"The alleged new element presented was a forward-facing video footage of car 14 which was unavailable to Aston Martin and the stewards at the time of the original decision - it was downloaded post the sprint session by F1," the stewards said.
"While the stewards had various other footage of the incident from different camera angles, they did not have this footage.
"In its written submission seeking the review, Aston Martin suggested that the new camera angle showed that the incident in question was a racing incident and not one for which their driver should be penalised."
The statement then went on to conclude: "Even though we did not have this footage at the time we made our decision, we did not consider the footage to be a “significant” new element.
"The new footage would not have caused us to question our decision or otherwise give us a perspective that we did not already have of the incident.
"There was sufficient footage from other camera angles to give us a clear basis to make the decisions."
Autosport understands the decision was communicated to Aston Martin on Friday, but because all Chinese Grand Prix stewards had to sign off in it and not all of them were available in a timely fashion, the publication of the verdict itself had to be delayed.
Speaking after the incident in Shanghai, Aston Martin team principal Mike Krack said the frequent penalties for his drivers, while other incidents weren't being punished, started feeling "not fair".
Alonso went several steps further in Miami after being caught up in a start collision in the sprint, suggesting Mercedes' Lewis Hamilton evaded a penalty for the incident because he "wasn't Spanish".
Alonso said he intended to raise the topic of fair application of penalties with the FIA.
