Gaston Ramirez volleyed Saints ahead after 15 minutes but City, struggling for form in League One, returned for the second half rejuvenated.
However, Jos Hooiveld's powerful header seven minutes from time ended City's hopes of a comeback.
"I am pleased with the way the players performed, pleased with the way we approached the game," O'Driscoll said.
"We got stronger as the game went on, which is pleasing.
"We came to terms with their possession, which you expect when you play a top team."
- Sports & Recreation
- Jos Hooiveld
- Stephen McLaughlin