Mercedes are considering disciplinary action – which could mean a fine or even suspension – against Lewis Hamilton after the three‑times world champion twice flouted instructions as his team-mate, Nico Rosberg, won his maiden Formula One world championship on Sunday.

Hamilton won the Abu Dhabi Grand Prix, his 10th win of the season against Rosberg’s nine and his fourth successive victory. But it was not enough to prevent the second-placed Rosberg winning the title by five points.

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Mercedes were angered by Hamilton’s refusal to respond to team orders to drive faster as he backed Rosberg into the drivers behind him, Sebastian Vettel and Max Verstappen; fourth place for Rosberg would have made Hamilton champion for the third year in a row.

Toto Wolff, the Mercedes head of motorsport, said: “Undermining a structure in public means you are putting yourself before the team. It is very simple. Anarchy does not work in any team and in any company.”

Wolff said he had not yet decided whether to crack down on a driver who has had 32 of his 53 race wins with the Silver Arrows since joining from McLaren in 2013. “The other half of me says it was Lewis’s only chance of winning the championship at the stage and maybe you cannot demand a racing driver that is one of the best, if not the best out there, to comply in a situation where his instincts cannot make him comply.

“It is about finding a solution as to how to solve that in the future because a precedent has been set. Let me sleep overnight and come up with a solution.”

When pressed again about what he would be doing about Hamilton, he thought for a while before adding: “We need to look at the overall situation and ask what does it mean. Everything is possible from ‘let’s change the rules next year because it does not work in those critical races and maybe we want to give them more freedom.’ Or we could have the more harsh side, that we feel the values were not respected. I am not sure yet where my finger is going to point or the needle is going to go.”

Wolff made it clear Mercedes were happy to let the two drivers race unless it compromised “our No1 objective of winning the race”.

Wolff said the team had calculated the Ferrari driver Vettel, shod with fresher rubber, had a chance of passing Germany’s Rosberg and Hamilton and stealing victory for the Scuderia.

The British driver said: “I did nothing dangerous so I don’t feel I did anything unfair. We were fighting for the world championship. I was leading. I control the pace. That’s the rules.

“I don’t know why they didn’t just let us race. There was never a moment I felt I was going to lose the race but it is quite clear, their thought process.”

Rosberg said: “You can understand the team’s perspective and you can enjoy Lewis’s perspective, There were many moments that were not enjoyable.”

The frosty atmosphere between the Mercedes drivers was evident before the podium ceremony. Rosberg hoisted the sport’s commercial supremo, Bernie Ecclestone, into the air but ignored Hamilton. The handshakes and congratulations eventually came on the podium.

Hamilton was supported by Wolff’s opposite number at Red Bull, Christian Horner, who had cheekily suggested a few days earlier that the Mercedes driver should employ the strategy. Horner said: “I wouldn’t have expected him to do anything different. He played completely within the rules.

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“Winning the race wasn’t going to be enough for him today, he needed cars between him and, if he’d charged off into the distance, he wouldn’t have created that possibility. So he won the race as slowly as he could. It’s like in a football game where the team might protect from the opposition by kicking the ball around and not enabling the opposition to get hold of the it. I didn’t see that he did anything wrong today.”

Horner, whose Red Bull dominated Formula One before the rise of Mercedes in 2014, added: “We know that Toto likes to control most things in the paddock, including other teams’ drivers. I understand that Toto has suggested that Lewis followed my instruction rather than his, and he should come and drive for Red Bull.

“Congratulations to Nico. He’s driven a great season and is a very worthy world champion. But it was naive to think there would be any different approach to this race with what’s at stake. Lewis drove a tactical race. He didn’t do anything dirty. He didn’t do anything against the rules. I think it would be unfair to criticise him for the way that he drove.”

However, Hamilton came under more fire after the post race press conference when he appeared churlish in defeat, prompting Vettel to praise his fellow German as a “worthy champion”.