The Scotland international scored his eighth Premier League goal of the season three minutes before half-time to seal the victory and take the Black Cats above Aston Villa into 15th place.
"We're all professional boys," the 25-year-old told reporters.
"We all know what is needed when we need to go and win game. I thought it was a good performance. We attacked well and defended well so you're always going to win games when you play like that.
"Sometimes it is not pretty and we ground it out. We needed the three points and we got that. We're just happy we got three points and a good performance as well."The three points gained at St Marys' could be crucial, particularly with the Christmas round of fixtures bringing clashes with in-form trio Manchester City, Tottenham and Liverpool. However, Fletcher believes that the nature of the win at Southampton will at least raise the spirits within the Sunderland squad.
"We approach [the games] with a bit of confidence," he added.
"We know we've got a hard Christmas period coming up but we've built a bit of confidence and we'll take that into the next game.
"The boys are all very tight. We all get on very well. It is a good bunch of lads. If we keep our heads down and keep working hard, we'll get results like this."