"Of the five draws we could have won two or three quite easily," the Blues boss said after the game.
"You could look at it another way and say we are unbeaten in six, including the League Cup.
"We have no divine right to come here and beat Southampton.
"Southampton are an established Premiership team having been there since day one, we've been in the top division only two years.
After carving out few opportunities in the opening 45 minutes Blues did have chances to have maybe nicked it in the second half. Darren Anderton coming closest to breaking the deadlock with a good volley that was well saved by Saints keeper Antti Niemi.
"The save was unbelievable, but if you have a predator on the pitch he taps in the rebound," said Bruce.
"But Anderton did well. This was only his second Premiership game since last January but he showed he can still play.
"We had a better chance earlier when David Dunn put one over the bar.
"We thought we had certainly done enough in the second half to win it."