Jesse Marsch’s side grabbed a vital three points on Sunday afternoon when they beat rock bottom Norwich City 2-1 at Elland Road.
The win, which was Leeds’ sixth of the season, means they have a cushion of four-points over the bottom three with nine matches left to play.
Leeds go to Wolves for their next outing, while their next game at Elland Road is due to come against Southampton in early April.
Kilgallon believes that as long as Leeds match their performance against Norwich then Southampton can be beaten, though he stressed that at this stage of the season it is points and not performances which matter.
“Southampton yes [beaten today] and heavily beaten by Villa as well weren’t they, 4-0”, Kilgallon said post match on BBC Radio Leeds.
“It’s another chance for three points and if they play like that they will pick them up, no doubt about that.
“But it is about getting the points, not about the performance.”
Southampton have lost their last three Premier League games on the bounce and are due to face Manchester City in the FA Cup before they then lock horns with Leeds at Elland Road.
The Saints edged out Leeds 1-0 in the earlier meeting between the two teams this season.
