Jesse Marsch’s side failed to take a good opportunity to win on Sunday when held to a 0-0 draw at Elland Road by Brentford.
Results over the weekend mean that Leeds are now just one point above the relegation zone in the Premier League, with a series of tough games on the horizon, starting with a trip to face Nottingham Forest for their next league fixture.
Kilgallon though is unconcerned by where Leeds find themselves in the table because he feels they have a strong squad at their disposal, even if he admits there are no certainties for relegation at the moment.
“I’m not worried because I look at that bench and those lads are strong. It’s decent”, Kilgallon said post match on BBC Radio Leeds.
“But then there are normally one or two teams that you are thinking they have gone [down already]. It’s a mental league.
“But I’m not overly worried because I think the squad is strong.”
Leeds have an FA Cup tie to tackle next weekend after getting past Cardiff City in the last round.
The Whites will play either Accrington Stanley or Boreham Wood, who play each other on Tuesday night.