Two goals from Marcus Rashford and Alejandro Garnacho in quick succession condemned Leeds to a 2-0 defeat to Manchester United at Elland Road on Sunday.
The game looked evenly poised before Rashford scored from a header in the 80th minute and Garnacho confirmed the points from the away side just a few minutes later.
However, Kilgallon believes that with a little bit of luck, Leeds could have got something from the game.
He admitted that when teams are struggling at the bottom end of the league table, they often do not get the rub of the green and it was the same for Leeds on Sunday.
But he stressed that the level of their performance shows that Leeds will be fine as long as they play at such a level consistently.
The former Whites defender said on BBC Radio Leeds: “When you are down there at the bottom, things don’t quite drop for you.
“[Crysencio] Summerville in the first half, he gets in around the back and the ball was sort of bouncing around and you are thinking, go on and poke it in.
“In the second half, it falls down from a corner and it doesn’t drop and this is what happens when you are down there at the bottom.
“But if they play like that, they will be fine.”
Leeds will hope to sort out their new manager before they take on Everton at Goodison Park on Saturday in what could be a crucial game.
