"It helps confidence and creates good habits, winning in the cup," said McLeish.
"The performance I'm not entirely pleased with but I didn't expect it to be smooth - we made a lot of changes and rotated the squad.
"But we soldiered on. When we went behind I thought we were going out of the cup. But I felt we had goals in us.
"If we'd gone two behind Southampton would have seen it through. But we got a lot stronger.
"It was a classic Bowyer goal, and Carsley has played a captain's role and got the winner."