Leeds kicked off life back in the Championship by playing out a draw with Cardiff at Elland Road on Sunday, but it was not easy going for the Whites.
The found themselves trailing the Bluebirds 2-0 by just the 39th minute, though did reduce the deficit quickly in the second half when Liam Cooper struck within four minutes of the restart.
Leeds laid siege to Cardiff’s goal as the half wore on and grabbed a 95th minute leveller through a superb strike from Crysencio Summerville.
The Whites are expected to be active in the transfer market before the window shuts and Kilgallon feels the final third needs attention as he believes the defence is good enough, though there is an injury doubt over Cooper, who was forced off.
Kilgallon said post match on BBC Radio Leeds: “It [signing a centre-back] all depends on Cooper, but [Charlie] Cresswell and [Pascal] Struijk, I like them both. Luke Ayling can go in there, [Ethan] Ampadu can drop back.
“You’ve got to think what can we do and what’s the most important position.
“I still think a striker that can get us goals.
“Watching that, it looks like Leeds this season are going to have a lot of the ball, so if there is some money there, spend it up on the top of the pitch.
“I think at the back there, I think it’s OK.”
Leeds are claimed to be trying to snap up Nathaniel Phillips from Liverpool to boost their centre-back options.
