Lillis, in temporary charge while Town find a replacement for Simon Grayson, halted the club's slide down the table with a vital three points.
"I have been in charge about a week now and it was all about getting in amongst the players and finding out what makes them tick, what their families are like," Lillis said. "If you get the respect of the players you have a chance."
Striker James Vaughan scored his fifth Town goal with a smart finish in the 65th minute to inflict defeat upon the club he enjoyed two loan spells with.
"That will do him the world of good," Lillis added. "Lee Novak scored on Saturday (against Leicester) and Vaughany scored tonight and they will take confidence from that.
"The confidence is starting to return to all the players and that's what happens when you work hard, tackle and fight.
"Neil Danns was shouting to me that his calves were cramping up and I shouted back 'that's good'. That's what I want - for players to come off with their tongues hanging out, all sweaty."
A win would have lifted Palace second but Town battled hard, with captain Peter Clarke immense at the heart of the defence. Adam Clayton's brilliant through-ball set up Vaughan, who had a loan spell at Selhurst Park, for a clever finish.
Before that Palace goalkeeper Julian Speroni twice denied another former Palace player, Danns. At the other end Yannick Bolasie proved a big threat and almost grabbed an equaliser in the fifth minute of stoppage time - but Alex Smithies produced a superb save.
There were reports tempers became heated in the tunnel after the contest and Palace boss Ian Holloway refused media interviews, and Lillis added: "We are two passionate managers. There were a few tackles around."
- Sports & Recreation
- James Vaughan