McLaren team principal Martin Whitmarsh also claimed Vettel was "lucky", but Red Bull boss Christian Horner said it was one of Vettel's finest drives.
"He drove a phenomenal race - you can see the number of cars he passed," Horner said. "It was one of the best of his career. He really went for it."
Mixed fortunes for McLaren drivers in Abu Dhabi
Ferrari team boss Stefano Domenicali said: "He did a great race. He had moments when he was lucky and moments when he was unlucky.
"He had a safety car at the right moment, which took his gap down from 22 seconds to 10 seconds. He was able to start last and finish third, so he maximised the situation and it was a perfect race for him."
Vettel's recovery drive meant he minimised the loss of points to Alonso, who is 10 points behind heading into the final two races.
Horner said: "We know how consistent Fernando has been this year. It was entirely predicable that, starting sixth, he was going to be on the podium.
"I had already mentally got an image of him taking between 15 and 25 points out of us, so to limit that to only three and finish behind him is a remarkable recovery and a great drive by Sebastian.
"Anyone who doubted he's a racer, he showed world class today."
Red Bull chose to start him from the pit lane to enable them to change the car settings to make it easier to overtake.
The field was twice closed up by the safety car, enabling Vettel to make up lost ground.
He damaged his front wing on the first lap but kept going, then benefited when a first safety car closed up the field, only to lose that advantage through his own mistake, when he veered to avoid Toro Rosso's Daniel Ricciardo during the first safety car period and broke his front wing against a track-side marker board.
Vettel then climbed back through the field, rose to second place behind eventual Raikkonen as the leaders made their pit stops, then dropped to fourth, 20 seconds behind, when making a second tyre stop.
That deficit was erased by a second safety-car period, after which Vettel passed McLaren's Jenson Button. He ran out of time to catch Alonso and Raikkonen.
Vettel described it as a "crazy race" and admitted the second safety car had helped him, but added: "The target was to win the race; it was only three cars ahead.
"Unfortunately I didn't get through Jenson as quickly as I did other cars but he had more pace.
"He defended very well, but I finally made it and he behaved very fair. You can't do that move with all the drivers."
Vettel delighted with battling third
Button said: "He did a good move around the outside. I could have run wide and we would have touched but it's not right, really.
"With the safety car, Sebastian 'lucked' in. He was on brand new option tyres [at the end] and I was on used primes [and so lacked grip]. It was a brave move considering his position."
Alonso said: "Sebastian made a lot of places, recovered well. He drove very well. There was a couple of safety cars that maybe closed the group, and this was out of our hands."
The Spaniard said he was "happy" to finish second when Ferrari had struggled for pace through practice and qualifying and that he was optimistic about his title chances.
"In the end it was a good weekend for us," he said. "Second was best possible result for us today; we keep fighting to the end."
Vettel said: "We have a very good car at the moment. The team is switched on and sharp; everyone is enjoying the moment.
"We had not always one of the best cars [earlier in the season] but good enough to score points, which is the reason we are here. I am looking forward to the next races. We have a fantastic chance. It is up to us."
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