The Briton had moved ahead of Rosberg, who started from pole, after the second round of pit stops, but the two drivers were on differing strategies: Hamilton had switched to the medium compound and was set to run until the finish, while Rosberg was on the softs and needed to stop again.
Mercedes asked Hamilton to move aside for Rosberg, but the Briton declined and after finishing the race in third, 0.5s ahead of the German, he explained why.
"I was in the same race as him - just because he had one more stop than me doesn't mean I wasn't in the same race as him," Hamilton said.
"And naturally if I'd have let him past, he would have had the opportunity to pull away and when he does pit, he's going to come back and overtake me, so I was very, very shocked that the team would ask me to do that, to be able to better his position.
"He didn't get close enough to overtake but I was never going to lift off and lose ground to Fernando [Alonso] or Daniel [Ricciardo] to enable him [Nico] to have a better race. So that was a bit strange."
Toto Wolff, Mercedes-Benz’s head of motorsport, said that the team will review the decision to ask Hamilton to let Rosberg by, adding: “We will do this calmly and work our way through any confusion or misunderstanding. There were so many things influencing the decisions we made and we must still determine whether we were right or not.”
Hamilton said that his anguish on Saturday, when he was eliminated at the start of qualifying because of a fuel leak, made his eventual third place all the sweeter.
"I can't express to you the pain that you feel when you have issues such as the issues that I've had in the last couple of races," he said.
"It's very, very difficult to swallow, and, to come back the next day and get the right balance between not attacking too much, and not making mistakes, all these different things…obviously when you're at the back you're having to push way past the limit than perhaps you would from pole position or in the top five.
"The fact that I've managed to come back through obviously is a showing of just how great this car is and how great this team is - but ultimately we've worked, I've worked, hard for it so it feels probably better than perhaps a win, gliding from the lead.
"It feels definitely much more satisfying when you come back through. And, as I said, to be ahead and to win the fight is really encouraging."
As a result of finishing third, Hamilton has cut Rosberg's championship lead to just 11 points - the duo on 202 and 191 points respectively. Race winner Daniel Ricciardo is third on 131.