Long met a Steven Davis cross just before half time but headed straight at Lukasz Fabianski in the Swansea City goal.
But after a pep-talk from boss Ronald Koeman at half time, Long went out in the second half and made no mistake as he connected with James Ward-Prowse’s cross to net the winner.
“The first one I thought the defender was going to head it away and he stepped under it,” Long told BBC Radio Solent after the game.
“If I had mishit it, the ball might’ve found the corner. It was just before half time.
“The gaffer said don’t worry another chance will come your way and thankfully James put in a great ball for me.
“You always want to score the goal and grab the headlines, but a lot more credit has to go to the defenders and Fraser [Forster].”
Swansea were looking to extend their own unbeaten run to five games against Saints, but Long felt the visitors dealt with the threat of Francesco Guidolin’s side extremely well.
“We know it’s a tough place to come, but we were confident in ourselves that we could get the three points,” Long added.
“But as you’ve seen we knew it wouldn’t be easy. They play some good football, they move the ball well and cause us problems.
“In the last five or six games we’ve been very solid at the back and the longer the game goes on with a clean sheet the more confident we feel.”