Fletcher's first half strike proved the difference in appalling conditions on the south coast as Martin O'Neill's side eked out a 1-0 win to make it two victories from their last three matches.
"We're all professional boys," the Scotland international said. "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."