Ferrari had racked up six straight pole positions, and shown impressive straight line speed, before Mercedes were back on top in the race in Austin with Valtteri Bottas winning from the front of the grid.
Ferrari were off the pace on Sunday while Bottas led team mate Lewis Hamilton, who clinched his sixth world title, in a one-two with Verstappen third.
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Formula One's governing body issued a technical directive before the race in response to a Red Bull query, ruling out a sophisticated way of increasing the fuel flow to boost performance.
Asked afterwards in a news conference whether he was surprised by Ferrari's lack of performance and could offer an explanation, third-placed Verstappen suggested they had been bending the rules.
"Not surprised, at all, about it. After what came out. So that explains everything," replied the Dutch 22-year-old. In a separate interview with Dutch television, he used the word 'cheating'.
Ferrari team principal Mattia Binotto said he was disappointed by the comments.
Sebastian Vettel (Ferrari) - Valtteri Bottas (Mercedes)
Image credit: Getty Images
He pointed out that Sebastian Vettel had missed pole by a mere 0.012 seconds and that Charles Leclerc raced with an old engine after problems in final practice.
"If we look at the race, certainly the speed on the straight was not our issue and we had clear problems with grip on the car on the first stint on both drivers," Binotto told reporters.
"I feel the comments are completely wrong and it is not good for the sport and everybody should be a bit more cautious," added the Italian.
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He had said earlier in the week that Ferrari's engine was completely legal and the team were annoyed by continuing paddock rumours.
Leclerc, who finished fourth and 52 seconds behind Bottas, said Verstappen's comments were 'a joke'.
"He has no clue. He is not in the team. I don't know why he is speaking, he doesn't know anything about us," said the Monegasque.
Vettel retired after eight laps of the race with rear suspension failure.
"I just had really, really poor grip and struggled to get the tyres to work and had a poor feeling with the car straight away," said the German.
Leclerc said the front left tyre of his car felt 'very, very weird' in the first stint.