Leeds are still looking for a new man to take charge at Elland Road after sacking Jesse Marsch, amid a run of poor results.
Michael Skubala is standing in as caretaker boss and has led the side to a draw and a loss against rivals Manchester United.
Former Ajax coach Alfred Schreuder is now the front-runner to take charge and he was at Elland Road on Sunday.
And Kilgallon has insisted that with the makings of a good squad at Leeds, it is essential the club get the next manager right.
“I think there’s a good squad there and they need to get the right manager in”, Kilgallon said post match on BBC Radio Leeds.
“This is a big call now for Leeds United and it needs to be right.
“I think you can do something with that squad.”
Leeds pushed Manchester United hard in the Premier League encounter and only suffered defeat due to conceding two goals in the final ten minutes of the game.
