During his stint as musical guest on the sketch show, the 45-year-old singer had a special guitar that was placed in the background during his first performance of his Beyonce collaboration, "Don't Hurt Yourself".
Taking to his Instagram account ahead of the broadcast, the musician shared a closer look at the guitar, which was made specially in honour of the Van Halen frontman, 65, who lost his battle with throat cancer last Tuesday.
"I thought it could be a nice gesture for me to use this blue Eddie Van Halen model guitar for one of the songs tonight on SNL. The guitar was designed by Eddie (with a few customisations I had added)," Jack explained, sharing photos from the making of the guitar.
"Eddie was very kind to me and saw to it that this guitar was made for me to my specs. I won't even insult the man's talent by trying to play one of his songs tonight," Jack continued, adding, "Thanks again Eddie for this guitar and rest in peace sir."
Jack replaced country music star Morgan Wallen on the show, who was dropped as musical guest after the maskless star was photographed partying with fans and kissing random girls following a University of Alabama football game on 3 October.
Despite dropping Wallen, "SNL" boss Lorne Michaels said he didn't hold a grudge against the country musician and promised to invite him another time.