After claiming a 1-1 draw against Manchester United last weekend, Wolves went out of the Carabao Cup on Tuesday night after falling to a penalty shoot-out defeat to Leicester City.
But Costa is urging his teammates to concentrate on the return of Premier League football to Molineux on Saturday when Wolves host the Saints.
“It’s always difficult to go to Old Trafford. They’re a big club, but we knew what we had to do and we weren’t going to lose our identity. We went there and achieved a positive result, we could have even got a victory.
“I am also aware that every one of my teammates could enter the line-up at any moment and will do things well. This rotation means we’ve always got to be at our best and I want to continue like that, playing at my highest level.
“I don’t see that as a competition, but that a player has come in and improved the quality in our team. But we know that if things aren’t going our way, we’ve always got another thing up our sleeve.”
Wolves have received praise for the way they have been playing since the side arrived in the Premier League, and the forward said the players will maintain their attractive style going forward.
“We won’t change our identity for no one,” Costa said. “That is how we are going to continue. We know that they [Southampton] are a good team with good players that play well, but we know what we have to do and we’ll do that until the final whistle.
“We aren’t going to change anything. We're going to focus on what we have worked on, play our game and continue what we have done so far. If we do that, we can get the three points.”