The Hoops gritted their teeth and showed their mettle to tile rivals Rangers by going within a point of first place with a brilliant 4-0 away victory at Rugby Park over Killie.
Shiels admitted that Celtic were far and away the better team on the night and also praised their fans for showing so much support for manager Neil Lennon who is again in the headlines but this time for having more suspicious parcels sent his way.
"There were influential factors in the way Celtic played and the manager must be very proud tonight," Shiels said.
"They got an early goal which set the standard for the rest of the evening.
"When I heard my reaction was disappointment and sympathy for him, he is in the same profession as I am and I don't want anything to happen to anyone.
"I know if I was playing for someone, I would be doing my utmost to show I was supportive of him and that's exactly what the Celtic players did tonight.
"It's the best performance that I've seen from any team this season in the SPL.
"They were crisp in their passing and clinical in their finishing, it was a massive performance and we couldn't get near them at times.
"I don't want to take away from the quality, they produced that because they have that in them.
"I have never heard the Celtic support like that. Not only were the players supportive of the manager, the supporters played their part too and the quality they produced was the icing on the cake."