The German won his maiden world title last weekend at the Abu Dhabi Grand Prix after finishing second to his Mercedes team-mate.
Hamilton had tried to slow the pace to allow rival drivers to catch his team-mate, but Rosberg eventually held on despite the immense pressure.
Rosberg won the drivers' title by five points and he admits the former McLaren star was probably in the form of his life.
He told Sky Sports: "It's not possible you do the same performance as if you're in Lewis' position who has nothing to lose.
"It became clear as well, that's why he got all the pole positions and I was second in the last couple of races. It's because he's free, has no weight [on his shoulders], nothing to lose. I think it was the best Lewis I've ever seen in those last few races as well.
"He was not only completely free, but the most motivated and determined ever, working as hard as ever. Difficult to beat him in those circumstances."