Two divisions separated the sides last term but Phil Parkinson's side are back in the second tier for the first time in 43 years after securing an historic third successive promotion while the Hampshire outfit were relegated from the Premier League.
Although Southampton are tipped to go straight back up, summer signing Windass insists the teams start as equal this season.
"We're playing against a top side but it's up to us and the manager to combat that and try to get the best result we can," said the attacking midfielder.
"We are in the same division for a reason.
"I don't look at Southampton as an ex-Premier League team when I'm going down there on the opening day of the season, or be impressed by that.
"I just look at them as another team in this division that we're going to try and beat.
"They had what they did last year and didn't win many games so they're coming into the season with not much confidence.
"If we can go there and implement our game plan and get our players on the ball and do what we can do, I'm sure there's a lot of players in the same bracket as me that know we can go there and (cause) what seems to be an upset but I don't think it would be."
Windass is one of eight new signings brought in over the summer after leaving troubled Championship rivals Sheffield Wednesday by mutual consent and the 31-year-old is optimistic about the Reds' chances this season.
"We've signed players who are historically top players in this division who also have ambition, who all want to be the best they can be along with the current players who have obviously been incredible for three seasons," he said.
"Hopefully we can all gel together and create a really strong Championship team and really push for what we are here to do."
Windass made his Wrexham bow in the second of back-to-back matches against FC Groningen in the Netherlands last weekend, getting a run-out which was much needed.
"It was just nice to get on the pitch," he said. "I've not played any minutes at all in pre-season with the situation at Wednesday and moving clubs.
"To get a game was nice a week before the first real game and hopefully I can start off as good as I can."
Wrexham lost 3-1 but Windass opened his account for the club with the equaliser when he found the net with a superb finish from George Dobson's ball into the box.
"As a player who plays at the top of the midfield, I like to try get as many goals as I can," he added.
"Obviously my main focus is just helping the team in creating and scoring, but I'll leave that pressure up to the strikers.
"If I can contribute as many goals as I can, that's always nice."