Goals from Murray Davidson and Gregory Tade saw Killie slip to a second defeat in six days following their Scottish Cup exit to Hibernian.
Shiels said: "I'm disappointed for our supporters who made the journey on a cold day. That is twice in six days we haven't delivered.
"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."
Shiels now knows his side have their work cut out to secure a top-six finish and believes Killie have not been helped by a hectic schedule in February.
"This puts us in a position where we have to win our last three games before the split," he said.
"We played six matches in February and now have three weeks off in March. It is hard to fathom."