"I just remembered how it really was," he added.
"There were a lot of places like that in the early '60s ... you wouldn't want to live there now," Charlie Watts said.
The Stones also re-created their recording studio, complete with original instruments, for Exhibitionism - The Rolling Stones, the band's exhibit that debuted at Industria in New York City on Saturday after launching in London earlier this year. It includes colorful tour outfits, Jagger's lyric book, Keith Richards' 1963 diary, Watts' toy drum kit and various photographs, from posters to magazine covers.
"None of it made me cry particularly. Some of it made me laugh," Jagger said of the memorabilia.
The exhibit run in New York through March 12, 2017. Some of the pieces are works by Andy Warhol, Alexander McQueen and John Pasche, who designed the Stones' iconic tongue logo.
"It's like bumping into memories everywhere you look for me," Richards said. "You turn the corner (and say), 'Oh, that's where I left it. Whether it's a guitar or a piece of clothing, everything sort of rings a bell somewhere."
Ronnie Wood, who joined the group in 1975, said he enjoyed seeing the "little motifs" throughout the exhibit, and added that one of his favorite memories was joining the band for his first public performance - on his birthday.
"I had to learn the entire Stones back catalog to get ready to go onstage on June 1, my birthday, for my first public show with them," he said, smiling.
Of his highlights, Richards said, laughing: "I can pick out a few lows but we won't bother with them, but otherwise, it's been pretty much a high all the time."
The Stones will release a new album of blues cover songs called "Blue & Lonesome" on Dec. 2. When asked what his future goals are for the band, Watts said: "Staying alive I think is the biggest thing at the moment, or getting up in the morning."