Celtic rounded off a momentous week with a convincing Clydesdale Bank Premier League victory at Rugby Park, following on from the 2-1 home win over Spartak Moscow on Wednesday night that sealed their place in the last 16 of the European competition.
Scott Brown fired them into the lead in the 27th minute this time out, before second-half goals from midfielder Joe Ledley and substitute Georgios Samaras, on for Lassad Nouioui, rewarded the Parkhead side's dominance.
Former Hoop Cillian Sheridan grabbed a late consolation.
Celtic have struggled at times in post-European games this season and indeed had taken only one point from nine following their previous three Champions League games, including a 2-0 home defeat to Killie in October.
However, there was no such danger this time as Neil Lennon's side cemented their place at the top of the SPL, and Shiels believes that is ominous for the rest of the league.
He said: "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."