Second-half goals from vice-captain Murray Davidson and substitute Gregory Tade wrapped up the points for a dominant Perth outfit.
Shiels admitted: "I'm disappointed for our supporters who made the journey on a cold day. I felt we shaded the first half play but there wasn't much goalmouth action.
"At half-time we said if we pushed on we could win the game. But it was poor, poor play to give away a corner and then no one picked up Murray Davidson for their goal.
"When you prepare for a football match you go into specific details and it is so annoying."
Coming hard on the heels of a Scottish Cup defeat against Hibernian, Shiels said: "That is twice in six days we haven't delivered."
Reflecting on his prospects of a top-six place, the Irishman said: "This puts us in a position where we have to win our last three games before the split."