Scott Robertson's opener was cancelled out by Lee Ashcroft on his first Killie start but Doyle was at the double to ensure Hibs leapfrogged their opponents and moved into seventh place.
Shiels said: "I felt we were the team who were most likely to win the game and we were going for the winner.
"It looked like we were going to win the game if there was going to be a winner.
"Then, unfortunately, we conceded two late goals and Hibs have gone home happy.
"Good luck to them but we will certainly not be doing the lottery with the way things are going. We have to take it on the chin and move on."
Meanwhile, Shiels is sweating over the fitness of Ross Barbour, who was carried off with an ankle problem.
He said: "We don't know how he is yet. He is in the hospital for an X-ray and we haven't got the results of that.
"The swelling was quite quick, which wasn't a good sign. We don't know the outcome just yet."
- Sports & Recreation
- Lee Ashcroft