Both sides looked deflated after disappointments in the past week, Arsenal losing to Chelsea in the League Cup final on Sunday and Blackburn being knocked out of the UEFA Cup by Bayer Leverkusen last Thursday.
Despite Arsenal having the better chances, it was substitute McCarthy who broke the deadlock with a superb right-footed shot from the left after a David Dunn pass.
"The goal itself deserved to win any game," Blackburn coach Mark Hughes told Sky Sports News. "It's a goal of world class quality."
Arsenal's appeals for a penalty mid-way through the first half looked justified when Brett Emerton brought down Freddie Ljungberg.
They were also left to rue other chances, Julio Baptista squandering Arsenal's best opportunity in the first half when he had a free header from six yards that he sent over the bar. He was also denied a couple of times by Blackburn goalkeeper Brad Friedel in the second half.
"We had the chances to score the goals but we didn't do it and then of course we made the fatal mistake," Arsenal manager Arsene Wenger told Sky Sports News.
Blackburn face Manchester City at home in a quarter-final on March 11.
