Sean Dyche's side sprung one of the surprises of the season at Turf Moor, as George Boyd's sweetly struck half-volley earned them all three points against the defending champions.
That victory leaves Burnley 18th in the table, just one point from safety ahead of the trip to St Mary's Stadium, and Dyche knows there is plenty of work still do if his side are to avoid the drop.
"We are aware of the league but we don't stare at it," he said. "Our learning curve has to come to fruition and it has to come to fruition in the last nine games.
"We've got nine big games coming up and we keep working hard. The basics have to be instilled in the team and delivered.
"The one thing I've learned is that there is no guarantee where you get your next result. It was a good performance against City, and we're going to have to do that again.
"Southampton are a good side and have had a good season. They've had many players perform this season. It will be a big challenge for us."
Defender Michael Duff was recalled to the line-up against City in place of Michael Keane, and the former Northern Ireland international says the victory has given everyone at the club an extra bit of belief.
"The result last weekend gives everyone a big lift, especially with the performance as it was, but it's only three points," he said.
"I think we have surprised a few people along the way and it's just having that belief now."
Southampton come into the clash in sixth place, buoyed by a much-needed win over Crystal Palace and Sunday's 1-1 draw at league leaders Chelsea, which followed back-to-back defeats to Liverpool and West Brom.
Ronald Koeman's men are one of just five teams to lose to Burnley this season - Dusan Tadic's penalty miss proving crucial as Ashley Barnes went on to the net the only goal at Turf Moor back in December.
"It's a different game, a different system that they play, more direct, and it will be difficult," Koeman said.
"They beat us but it was not a very good game on that day. We missed a penalty and we got a stupid goal against us.
"What we do realise is that it's a different one [match]. Burnley are doing well the last few weeks, they had some great results against Chelsea and Man City last week and they will make it very difficult."
Koeman welcomes Eljero Elia back into contention after he missed the draw at Chelsea with an ankle problem, while Burnley have no new injury worries, with Matt Taylor (Achilles) still not quite ready for a first-team return.
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