Hull's third-choice goalkeeper, who continued to deputise for injured duo Allan McGregor and Steve Harper, kicked a seemingly straightforward clearance straight to Victor Wanyama - who subsequently hit a wonderful 40-yard effort into the empty net.
The home side improved after that goal, although Southampton goalkeeper Fraser Forster was seldom tested.
Bruce admits Hull fell well below the required standard at the KC Stadium, although he feels there could have been a different outcome had they not been chasing the game early on.
"It's a great finish from Wanyama, but you make a mistake like that and it puts everyone on their heels," he said. "It was a difficult afternoon for us.
"We've seen it happen. To go 1-0 down to a goal like that is difficult to take in for everyone; it shocked the whole stadium, the players and everything.
"But you make mistakes and this year, if we're going to be honest, individual mistakes have cost us big points.
"You have to say it's a wonderful finish; when the ball comes at that speed sometimes they end up over the bar and in row z. It made life difficult for us."
On his team's performance, Bruce added: "The first half there was nothing in it; it was two sides playing well.
"It was when we went chasing the game that we lost the discipline to take care of the ball and lost the possession we had in the first half.
"The longer it went the harder it became for us and the easier it became for them."
