Hamilton chased Rosberg throughout the first half of the race before both cars began to slow with an energy recovery system problem.
The Briton then jumped Rosberg in the second pitstops as they both rejoined behind Felipe Massa's Williams - which was on an alternate strategy - but Hamilton immediately ran into brake trouble and had to retire.
"I was following him and when you're following someone you're gaining more heat," said Hamilton of his pursuit of Rosberg.
"He was in clean air all the time in front.
"There was not much I could do. When I came out in front, everything was cooked already."
Hamilton said he was informed soon after his first pitstop that both he and Rosberg had mechanical problems.
"We knew as a team that we had some issues in the second stint, but we thought we would be able to manage it," he said.
"I got him in the stop and was thinking 'finally, wow, what an amazing feeling'. Then straight away on that lap the brakes failed."
With Rosberg nursing his car home second behind the winning Red Bull of Daniel Ricciardo, Hamilton is now 22 points behind his team-mate in the 2014 Formula 1 standings.
"The team still got 18 points so we'll move on and hope we don't have any more DNFs," said Hamilton.
"I've had a lot of work to do since race one [when he retired in Melbourne]. That's now two DNFs I've had and none for Nico.
"We'll keep pushing and I'll come back stronger."
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