Peaty, bidding to become only the second male swimmer after retired US great Michael Phelps to win the same title at three successive Games, took silver together with Nic Fink of the United States.
Their time of 59.05 was just 0.02 of a second slower than Martinenghi.
The Italian told RAI television he had closed his eyes and hoped for the best.
"I showed that the time doesn't matter, it matters how you are, seizing the moment," he said.
Peaty had swam 58.86 on Saturday, some way off the 57.94 he produced at the British championships in April. He holds the world record of 56.88 set in Gwangju, South Korea, in 2019 plus the Olympic record of 57.13 from Rio 2016.
"I gave it my absolute all," Peaty told the BBC. "I executed it as well as I could. It's not about the end goal, it's about the process.
Peaty started in lane four after powering into the final with the fastest time on Saturday, but he was second at the turn and it came down to a matter of milliseconds and a stroke or a glide at the finish.
"It doesn't matter what time it says on the scoreboard. I think in my heart I have already won. I'm so happy that I can race against the best in the world and still come joint-second," he said.
