The German declared the race was far from enjoyable describing the pressure as the most intense he has ever experienced.
“It is an incredible and unbelievable feeling,” said Rosberg of winning the title.
“The race was so horribly intense.
“It was definitely not the most enjoyable race I've ever had.
“There was no chance to overtake Lewis (Hamilton). I was just stuck with the guys behind catching us, it was horrendous.
“It is a relief that it is over. It is not possible to explain the intensity, it was a horrible feeling out there.”
Rosberg's triumph sees him follow in the footsteps of his father Keke Rosberg, who won the world title in 1982.
The 31-year-old has become only the second son of a world champion after Damon Hill to lift the title.
Reflecting on his achievement, Rosberg paid tribute to his parents for their role in his rise to the top of F1.
“Every Saturday night I get a message from him (Keke), like ‘pedal to the metal tomorrow', that is his words of advice. My dad and my mum are such a big part of this,” he added.
“My mum on the private side and my dad for my career steps. It is massive. It is good how he is letting me get on with it. It feels right, him stepping back a bit for sure.”