"I thought it was stupid," McCain said on CNN's "State of the Union." "I thought it was horrifying."
The magazine's decision sparked strong public backlash, with many saying the cover was insensitive to the victims. Three prominent New England-based businesses - CVS pharmacies, Stop & Stop, and Tedeschi Food Shops - announced they would not sell that edition.
But others, including the magazine itself, defended the decision, saying the story is about how a young man popular with his friends became someone who could perpetrate such a violent act.
"The fact that Dzhokhar Tsarnaev is young, and in the same age group as many of our readers, makes it all the more important for us to examine the complexities of this issue and gain a more complete understanding of how a tragedy like this happens," the magazine said in a statement.
But McCain said it was "inappropriate" for the magazine to prominently feature someone who's "responsible for the taking of innocent lives.
"But for me to tell them to pull their magazine from the bookshelves, at newsstands, it's not up to me to do that. I think most Americans surrender to judgment on that," he told CNN Chief Political Correspondent Candy Crowley.
"Rolling Stone probably got more publicity than they've had in 20 years," he added.