A 2-0 defeat at home to Manchester United left Leeds 17th in the Premier League and they are perilously close to dropping into the relegation zone.
However, Leeds earned plaudits for the attitude and industry they displayed in the back-to-back games against Manchester United.
Kilgallon indicated that it is mildly annoying to see the Leeds players show so much gumption against Manchester United while being poor in other games.
He understands the importance of the games against the old enemy, but insisted that the same spirit needs to be on display when Leeds visit Everton on Saturday.
The former White is certain that Leeds can beat Everton and overrun them if they show the same attitude at Goodison Park.
Kilgallon said on BBC Radio Leeds: “It’s frustrating, they put a shift in.
“They’ve just got to have the same attitude now against Everton.
“I know it’s Man U, you raise your game and they know how much it is for the fans to beat Man United and it’s a big game.
“Play like that against Everton and I’m sure they will overrun them and the quality will show.
“Everton, coming up next, a team that we’ve got to beat.
“That’s for sure.”
Leeds remain without a permanent manager, with caretaker boss Michael Skubala to be at the helm at Goodison Park.
