The seven-time world champion completed the podium behind Fernando Alonso and dominant race winner Max Verstappen, who claimed Red Bull's 100th championship win by 9.57 seconds.
Hamilton enjoyed a strong launch and initially jumped front-row starter Alonso into the first corner.
He then stayed ahead through the first round of pitstops - notably escaping any penalty for a potential unsafe release that forced the Aston Martin driver to hit the brakes.
Alonso continued to give chase and was able to reclaim second place with the aid of DRS into the last chicane on lap 22 of 70.
While Hamilton was able to close to within two seconds during the final stint, Alonso responded by dropping his lap times to cement the runner-up spot.
Hamilton reckoned Mercedes lost out to the AMR23 - which sported new sidepod bodywork and a revised floor this weekend - through the low-speed corners that dominate the Montreal lap.
He said: "Unfortunately, we didn't have the pace today. We knew that this weekend, this wouldn't be our strongest circuit as we struggle in the lower speed corners particularly.
"That's really where I was losing to Fernando and to Max, just on traction out of Turn 2, out of pretty much every corner.
Lewis Hamilton, Mercedes-AMG, 3rd position, celebrates with his team in Parc Ferme
Photo by: Glenn Dunbar / Motorsport Images
"But we've got a lot of work to do just to add rear downforce to the car, and a little bit more efficiency.
"But we're chipping away as I said, and I do believe we will get there at some stage.
"Max was a little bit gone. But I think our pace was a little bit closer today. So, we're going in the right direction."
Seven-time F1 title winner Hamilton, who said it was an "honour" to share the podium with fellow world champions Alonso and Verstappen, added that Aston Martin had been a "little bit of a step ahead" of his Mercedes team throughout the Canadian round.
He continued: "Honestly, it's been a great weekend for us. I think we are slowly chipping away. I think the Astons took a little bit of a step ahead this weekend when they added the upgrades.
"But we're working on bringing some more moving forwards."