"Lewis is doing a great job as it is," Button said. "As always, I go out to win. I'm not going to go out and pedal round and sit behind my team-mate."
Hamilton's victory moved him up from fifth to second in the championship while Alonso finished third. The two Red Bull drivers Sebastian Vettel and Mark Webber, who went into the race second and third in the table, failed to finish.
The Spaniard fought up through the field to finish third in the race.
"Looking at the championship," Alonso said, "we say we need to concentrate [at each race on] who is second. It was Vettel yesterday and we were happy for the McLarens to be strong this weekend. And yeah, the race went like a movie for us, like a dream."
He added: "McLaren have won the last three grands prix and they are in top form.
"[I was asked] in winter testing who is the driver I respect most and that was Lewis and we're still here, 13 races afterwards, we are first and second in the championship. It will be tough until the end."
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