The Dutchman was all over Hamilton on the penultimate lap at Suzuka, as the race leader got bogged down lapping the squabbling Felipe Massa and Fernando Alonso.
Verstappen then dropped time clearing both drivers and ended up 1.2s adrift at the chequered flag.
"I could see Lewis managing his tyres and, with traffic, it seemed difficult for him to follow other cars compared to me," said Verstappen.
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"When you close up, you lose a lot of downforce. I couldn't really attack him, but I tried.
"It didn't help, but it was more last lap with Massa.
"But I don't think I could get past Lewis, I could close up.
"It was not ideal but it wouldn't have made a difference."
Verstappen overtook teammate Daniel Ricciardo at the start and quickly moved past the hobbled Ferrari of Sebastian Vettel.
Last week's Malaysian GP winner could not match Hamilton's pace in the initial run on super-softs but a "better balance" on softs and a late-race virtual safety car facilitated his late-race challenge.
"Once I got past Seb I could do my own thing," he said.
"The first stint was all right, Lewis was a bit faster, and then on soft tyres we had a better balance.
"I didn't want to close up [to Hamilton] too much in case [that] destroyed my front tyres and I needed them at the end."
Alonso was summoned to the stewards after the race for "ignoring blue flags" in that tense finish.
He said he did his best not to interfere, having finished outside of the points in 11th.
"They can do whatever they want," Alonso said. "I don't have points anyway.
"I tried not to bother anyone. They [Hamilton and Verstappen] were first and second with two laps to go and they finished first and second so I don't think it was determinant for the race.
"But whatever they say, we'll accept it."
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