Killie were pushing for a winner with the score at 1-1 before Eoin Doyle grabbed a late double to snatch the points for the visitors.
"I felt we were the team who were most likely to win the game and we were going for the winner," said Shiels afterwards. "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."
Killie's Ross Barbour was stretchered off in the first half with an ankle injury which Shiels admitted looked serious.
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."