Smith's last-ditch drop-goal on Saturday saw England end Six Nations champions Ireland's hopes of successive Grand Slams.
The 25-year-old came off the bench to make his first appearance of the tournament after recovering from a calf injury.
Smith has yet to cement his place as England's regular fly-half since making his debut under Jones in July 2021 and has been criticised for a perceived lack of consistency.
But Jones, who began his second stint as Japan head coach in January, said "it takes time to mature" as a fly-half and that Smith will be "reaping the benefits of the experience he's had".
"Look at most American quarterbacks now - they can play until they're 40," the Australian told reporters in Tokyo.
"We're seeing the same thing in rugby. Marcus Smith's best time is to come."
Smith had been expected to start England's Six Nations opener against Italy until he was ruled out with an injury he picked up in their training camp.
He was hoping to step out of Owen Farrell's shadow after his rival for the number 10 jersey ruled himself out of the Six Nations for mental wellbeing reasons.
Farrell was first choice in the position at last year's World Cup, with Smith converted to full-back.
Jones, who was sacked by England in late 2022, said fast-tracking Smith into his team was "one of the things that still I don't know whether it was a mistake or not".
"I wanted to change the style of England, I wanted to play a more aggressive, attacking style with Marcus there," he said.
"It just didn't fit the team at the time."
Jones returned to the Japan job after a disastrous 10-month spell in charge of his native Australia that saw them exit the World Cup at the pool stage for the first time.
His first game in charge of Japan will be in Tokyo in June against England, who he took to the World Cup final in 2019.
"The only disappointment is we're kicking off at three o'clock - I wanted to kick off at the hottest part of the day, which is two o'clock," he said.
"Unfortunately we can't do that. We're still going to have to make it hot for them."
