Five-time Formula One world champion Lewis Hamilton maintained Mercedes' record winning start to the season when he was handed the controversial victory courtesy of a disputed stewards' decision, despite crossing the finish line just behind the German, AFP reported.
Vettel was deemed to have forced a charging Hamilton toward a wall after running off at a chicane and rejoining across a strip of grass.
The Briton had to brake and pull out of his overtaking maneuver, prompting the stewards to impose the time penalty on Vettel.
"Where could I go?" protested Vettel.
"They're stealing the race from us."
Ferrari team principal Mattia Binotto later said the team would be appealing against the penalty.
"At the moment, we, as a team, are naturally disappointed," said Binotto in a statement posted on the Ferrari official website.
"As for Seb, I don't think he could have done things differently, which is why we have decided to appeal the Stewards' decision."
Under the sport's regulations, Ferrari has 96 hours from the end of the race to gather evidence to support its appeal.
Vettel drove his car back to the garage instead of into parc ferme and refused to attend the postrace interviews.
He stormed off to the Ferrari motor home before being persuaded by his team to return for the podium ceremonies.
On the way he walked into parc ferme and swapped the number one for the winner from in front of Hamilton's Mercedes with the number two in front of the empty space for his car.
The pro-Ferrari crowd booed Hamilton on the podium, but Vettel told them, "Don't boo Lewis – you should boo these decisions, not him."
It was a record seventh victory in Canada for Hamilton and the 78th of his career. It extended Mercedes' season-opening run to seven successive wins.
Vettel was classified second ahead of his Ferrari teammate Charles Leclerc.
Valtteri Bottas was fourth in the second Mercedes followed by Max Verstappen of Red Bull and Daniel Ricciardo of Renault.
‘Falling out of love’
Vettel said he is falling out of love with Formula One after the controversy in Montreal, The Independent reported.
"This is not the sport I fell in love with," said Vettel.
"We all sound like lawyers. It just gives no edge to the sport.
"I am a purist. I love going back and looking at the old times, the old cars, the old drivers. It is an honor when you have the chance to meet them and speak to them. They are heroes.
"I really love that, but I just wish I could do what I do in their time, rather than today. It is not just about this decision, but other decisions, too.
"I rejoined the track, Lewis had to react, but for me that is racing, and a lot of the old Formula One drivers, and people in the grandstands here would agree that this is part of racing.
"It hurts me today because it impacts my race result, but this is also part of a bigger criteria."
Britain's 1992 world champion Nigel Mansell was in agreement with Vettel.
"Very embarrassing," he tweeted. "No joy in watching this race. Two champions driving brilliantly, ending in a false result.
"What's Seb supposed to do? Crazy. The car stepped out. At that point he was a passenger."