The 2012 world champion and Marquez now share the lead of the '13 championship on 41 points.
Despite insisting he had not given up on his hopes of victory after qualifying - when he was more than one second slower than Marquez - Lorenzo said the younger Spaniard was simply beyond his reach during the race.
"I want to congratulate Marc, for his record, the youngest winner in history," Lorenzo said. "He was the best today – phenomenal.
"Yesterday I was so far from Marc and Dani [Pedrosa], but we found something in the morning warm-up, in the slower corners.
"It wasn't enough. Today third position was the best we could do."
Lorenzo insisted he was not too disappointed with his podium finish given his belief that Austin favours the Hondas over the Yamahas.
"Winning is winning, third is third," he said. "Anyway we tried our best.
"This track is probably the worst for us, so finishing third, so close to victory, was something didn't expect yesterday.
"Unfortunately we needed two tenths we didn't have."