Hamilton led a Mercedes one-two after a thrilling battle with Rosberg, who attempted to pass his team-mate several times during the race.
Rosberg had the faster, softer tyre in the final part of the event, and Hamilton admitted he had to work very hard to keep the German at bay.
The former world champion accepted Rosberg was the faster of the two Mercedes drivers.
"Winning the race is the greatest thing, you are happy, but deep down inside I didn't have the pace today," said Hamilton.
"So we have to learn and find out why that was. A lot of the advantages I had in the last race, Nico found them when we came here.
"He did better than me and I have to see if I can improve.
"For me it was one of the toughest situations I have been in for a long time. The option tyre I believe is worth 0.65 [seconds per lap], so to hold him behind was very, very hard.
"I was pushing flat out for 10 laps, it was an exceptional race today, me and Nico haven't had a race like since since karting days."
Hamilton said, however, that he felt fantastic after having managed to use all his racing skills to take victory.
"There were a lot of times he was in my blind spot and no idea he was there," he added.
"I think it feels like a long time since I have been able to have a proper race and really use whatever skills I have acquired over the years, as a youngster in karting.
"Being able to go out there and use it again, it was a fantastic feeling. It is one of the greatest feelings in the world."
Rosberg, who finished a second behind Hamilton, said Mercedes had not imposed any team orders, and claimed he never felt they were taking unnecessary risks despite the intense battle.
"I was well aware the whole world thinking of team orders, but it was not that at all," Rosberg said.
"It was just 'guys make sure you get these cars to the finish'. The message was clear.
"We raced hard but with necessary respect, we were free to race all the way.
"At no time was there was a risk of taking the cars out. It might not have looked like it on TV, but it was good close racing.
"I thought I got him about nine times, but he always got the run back on me.
"He just did a good job, and that is it. Lewis is a great driver and made it work, and next time I need to do better."
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