Jost told Fallon Tuesday about a Christmas party he attended a while ago at Murray's house. Jost and a friend wandered around the house until they came across a box.
"It was such a cool photo and there were like 10 of them. It truly looked like he was throwing them away I swear to god and I was like, 'He's not going to miss one of the 10 that he's throwing away, right?'" he continued.
"It felt like not stealing, it felt like one man's trash is another man's treasure," Jost concluded.
Jost also discussed how staying indoors with Johansson is the longest time they have consistently spent time together.
"We've been together for about 120 days which beat our previous record of, I think, five," Jost said before he started laughing.
Jost's memoir titled A Very Punchable Face, was released on Tuesday.
Moments from Scarlett Johansson's career