"All the lads are still really trying," Kilgallon told BBC Newcastle.
"Every day in training the boss is still working us hard - none of the lads are thinking we'll cruise now."
On a personal level, Kilgallon has emerged as a key member of Martin O'Neill's squad in the absence of fellow centre-halves
John O'Shea and Titus Bramble.
The 26-year-old was ruled out for a month and a half after picking up an ankle injury in January's 1-0 defeat by Chelsea, but following his return to the first team last month has featured in the last four games.
"I got an unlucky injury, I was back in the team and doing alright, but my ankle went and it was a case of here we go again," Kilgallon said.
"I had to be patient, but got back in and I'm trying my best to play as well as I can.
"I've had a lot of help off the other lads, they've made it easy for me, I'm doing alright and now hopefully staying in there is the main thing."
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