Lillis was in the dug-out following Simon Grayson's sacking on Thursday and he watched on as Chris Wood cancelled out Lee Novak's penalty.
He said: "I am the academy manager and I will go back to that when a new manager is appointed and support him all I can.
"It's a big job and a good job. This is a Championship club with a great stadium and a chairman who puts his money where his mouth is.
"It's a great job for someone and no doubt there were some managers or their spies in the ground looking on."
Lillis said he was pleased to remain in the competition and added: "A couple of the lads came in disappointed but we are still in the hat.
"Leicester for me are the top team in the Championship and to rest a couple of players and have to throw them on in the second half shows us respect. He had to go for the big-hitters."
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