Academy manager Lillis, 53, and professional development coach Steve Eyre were installed as temporary bosses following the sacking of Simon Grayson last week and prepared the side for Saturday's 1-1 home draw with Leicester in the fourth round of the FA Cup.
Huddersfield chairman Dean Hoyle has said there has been no shortage of interest in the vacancy, but is in no rush to appoint the club's fourth manager in as many years.
Lillis, who made 242 appearances for Town between 1978 and 1985, said after seeing Leicester striker Chris Wood cancel out Lee Novak's second-half penalty: "I'm obviously disappointed we didn't get the win, but happy that we are still in the FA Cup and delighted with the way the lads went about things.
"Hats off to the fans as well because they responded to our efforts the way I knew they would.
"The players are frustrated and disappointed not to have won, but we gave one of the best teams in the Championship a game.
"I gave them some loving, because sometimes they need an arm around them and to be given some self-belief.
"But I also told them that we have a chairman who is putting his money where his mouth is and fans who are paying hard-earned cash to come and watch, and when that's the case, you have to give something back. That's the way I was brought up."