The Clarets controlled things early on at St Mary's Stadium, despite a trek to Turkey in midweek for a Europa League qualifier, and were nearly in front through Aaron Lennon and Jeff Hendrick attempts.
McCarthy was responsible for keeping his side on level terms in a half that saw Burnley enjoy 58% of possession, but the Saints improved in the second 45 minutes and had some openings of their own.
Speaking to BBC Sport after the match, Southampton's first-choice keeper admitted that he was particularly pleased to have kept a clean sheet.
"They were the better side in the first half and we think we were better in the second half," he said. "I was just happy to keep the ball out the back of the net. It feels really nice to get a clean sheet in the first game."