And Naysmith knows such support will be vital as the team battle against the odds this season.
Naysmith played the last 10 minutes of Hearts' 2-1 win at East End Park on Saturday as a trialist after joining former team-mate Gary Locke's side for pre-season training.
The former Scotland left-back helped Hearts end a 36-year major trophy drought by winning the Scottish Cup in 1998 before departing for Everton in a big-money move two years later, and his introduction sparked a standing ovation from more than 3,000 Hearts fans.
With administration-hit Hearts starting the season 15 points adrift of their top-flight rivals and with a first team featuring just three players aged over 21, Naysmith knows they will need similar support throughout the season.
Naysmith, who made his Hearts debut aged 17, said: "It's not something I had thought about, but it just shows you that they never forget you, the Hearts fans.
"I was quite touched with the reception I got, it was a surprise and something I really appreciated.
"We knew there was going to be a big crowd, but the noise they made and how they got behind the team, that's going to be vitally important this year.
"It's important that with such a young team, the fans stick with them.
"We are hoping there are not going to be many, but there will be some days where things aren't going to go according to plan, and it's important to stay together.
"That's where the fans need to stay with the young lads and keep behind them, because it's difficult, young lads are being asked to do seasoned professionals' jobs.
"But they are technically very good and have grown up together, so that can work in their favour."
The 34-year-old, who was released by Aberdeen in May, cannot sign for Hearts because of their registration embargo but he could be set to look for a new club.
"In my own mind I want to make sure I can do a pre-season," he said. "It's gone well so far, two weeks in."