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Vettel dropped to the back of the field in the formative moments of Sunday's race when he was forced to pit for a new front wing following damage sustained in a first-corner incident with Max Verstappen.
The Ferrari driver, who has seen his 25-point advantage reduced to just 12 following Hamilton's victory at the Circuit Gilles Villeneuve, recovered to fourth, which included two passing moves on the Force India duo of Esteban Ocon and Sergio Perez in the closing laps.
But Vettel, the four-time champion, felt he had enough pace to pass Red Bull's Daniel Ricciardo, too, to steal the final spot on the podium here in Montreal.
"When you are last after six laps anything is a gain, but we could ideally have got on to the podium," Vettel said. "We lost too much time fighting through the Force India cars.
"I knew we could recover position because the car is quick, but you have to fight your way through the field which is a lot of work, and it's not easy.
"The imagination going into the race was of course a different one. The pace was there and the car deserved to finish higher up."
Vettel was not particularly slow out of the starting blocks, but as Valtteri Bottas dived underneath the German, and then Verstappen raced around the outside, the driver who had finished either first or second at every round of the season so far was suddenly on the back foot.
TV replays showed that the fast-starting Verstappen, who later retired with technical gremlins, had nicked the nose of the Ferrari at Turn One, but the stewards took no action.
Vettel's Ferrari team were also slow on the uptake after they failed to spot the German had sustained damage until the safety car - deployed after Carlos Sainz and Felipe Massa crashed out on the opening lap - pitted and the race resumed.
"I haven't seen it from Max's point of view, but obviously I was not expecting it," added Vettel. "I was focusing on Valtteri and I did not have anywhere to go because Lewis was in front. If I brake later I run into Lewis.
"Max took his chance on the outside and ran over our front wing. He did not do it on purpose because normally you would get a puncture so in that regard he was lucky he did not get one.
"We had damage on the front wing which we did not notice initially, so we missed a free pit stop under the Safety Car."
