Neil Lennon's visitors followed up Wednesday night's momentous qualification for the Champions League knockout stages with a ruthless win over Killie, who had only a last-gasp consolation effort from Cillian Sheridan to show for their efforts.
By that time, the Bhoys were out of sight after Scott Brown's opener and second-half goals from Joe Ledley and Giorgios Samaras had ensured a three-point lead at the top of the SPL with a game in hand.
Shiels said afterwards: "I think there is a distinct clarity for Celtic now as to how they are going to approach the next few months.
"You could see in their body language that there is a great relief in achieving what they have achieved and now they can concentrate on domestic football.
"I knew they were going to be very positive having fulfilled their ambition of qualifying for the Champions League (last 16). It has a big bearing on how they felt within themselves and you could see that.
"That is the best Celtic have played in a long time, I would say. It bodes badly on us as we have to play them in December and January."