What could have been a huge setback in his bid for a fifth drivers' title turned into only an eight point deficit with still more than half the season remaining.
Finland's Raikkonen, who was handed a 10-second penalty before finishing third, admitted he had made a mistake, while Vettel said it is "quite silly" to think there was anything deliberate.
Hamilton also explained why he did not participate in the parc ferme interviews, conducted by Martin Brundle, in which Raikkonen offered his apology.
"I barely had any energy at the end to stand, let alone talk.
Who's he to judge what a driver is doing in the vehicle, I can accept it from Jacques [Villeneuve, Sky Italia pundit] because he's been a driver, but that person? No". "I would struggle to be that precise to take somebody out".
"Getting back to second is huge for us and I am happy with the drive. I'm grateful the vehicle was in one piece and I'm grateful to get through".
"This is the greatest race of the year and this is the greatest crowd so I'm sorry I could not bring it home for you".
A poor start when the lights went out allowed Vettel and fourth placed Mercedes team-mate Valtteri Bottas to sweep past by the first corner. It was first triggered when Raikkonen tagged Hamilton, sending the latter into a spin.
But there was no doubting the comeback.
It appeared Hamilton's Mercedes was permanently beached, then, first with all the alacrity of a Walrus dragging its tonnage across the sand, then like a thief running from the police he returned to the race. He fought back to sixth - after passing 12 cars in only 10 laps - which then became third after Marcus Ericsson crashed out at 200mph and the safety auto was deployed. This time it was the right call to favour track position.
Bottas assumed the lead, and no sooner had the racing begun when a second safety auto was issued following Romain Grosjean's collision with Carlos Sainz.
Hamilton recovered to second, aided by Mercedes decision not to pit him for fresh tyres under a safety auto to gain track position, but looked tense alongside Raikkonen while the top three waited to go onto the podium post-race.
"I think we need to improve our vehicle until the end of the year, that will be key because then you have something to fight, and if you have something to fight and something to play with, you can make things happen". If I'd followed them in I'd have finished behind them. But Vettel, on fresher and softer tyres, had too much. I didn't have anything left when I came in.
Asked what caused the neck problem, Vettel joked: "Maybe it's the stewards' fault from last week".
"Here In Their Home", he said in Italian to his team over the radio. In France, I lost my wing so I screwed my race. "What an incredible day".
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