Goals from Rickie Lambert, Guly do Prado, Adam Lallana and Richard Chaplow, made it Saints' best start to a season in 103 years.
Chris Wood pulled one back for Blues but Chris Hughton's side never really looked like breaking their away duck.
"We contributed to our own downfall in first half," said the Blues boss.
"The penalty gave them the momentum. I'm not taking anything away from the second and third goals, though.
"They were disappointing goals to concede from our point of view.
"The quality of the finishing was the difference between the teams."