Saints achieved automatic promotion from the second tier last season thanks in no small part to having the best home record in the division.
After home defeats to Wigan and Manchester United, the south coast side picked up their first Barclays Premier League victory at home to Aston Villa in their last match at St Mary's.
Adkins is hoping for a similar result when Martin Jol brings Fulham to Hampshire on Sunday, although the Saints boss knows the west Londoners will be no pushovers.
"It is a match we can lose, but it is a game we're going to look to go and win," he said.
"You have to be positive at home. We have been very good at St Mary's over the last few years and again starting this season.
"The atmosphere in the last home game when we beat Aston Villa 4-1 was electrifying. It was fantastic.
"The supporters lifted the players, the players lifted the supporters so everyone was together as one.
"We produced an excellent performance and got an excellent win. We're under no illusions, though, as Fulham are going to be a tough team to beat.
"We don't think we're just going to turn up and going to win. Fulham have had a very promising start. They're very organised, have good players and have won games this season.
"We know we've got to be at the top of our game, like every game in the Barclays Premier League, but we've got to go and look to win our games at home."
Southampton's performances so far this season have belied their three-point haul, with Rickie Lambert leading a particularly exciting attack.
However, their defence has been worryingly porous and they have conceded a league-high 18 goals already.
Adkins knows they need to tighten up quickly but will not be turning his back on their attacking mindset.
"We've led in four of the games so far this season," Adkins said. "We've done very well and have a mindset that we can go and score goals. We're very positive.
"But likewise we have to accept that at this level, keeping clean sheets is going to be very important.
"But when you look at, for example, Manchester City I don't think they've kept a clean sheet. If you look at Liverpool at this moment in time, I don't think they've kept a clean sheet.
"It's a situation that is not just ourselves. The games we have played have been a great challenge and ones we have really embraced and enjoyed.
"But it is about getting points on the board as well without going against the principles you've got."
Adkins may be able to welcome back Morgan Schneiderlin against Fulham after a knee injury kept him out of last weekend's 3-1 defeat at Everton.
The French midfielder was back in training today but Jack Cork faces up to a further five weeks out with an injury to his left knee.