Killie were ultimately undone by John Sutton's fifth-minute goal and Shiels was critical of centre-back Mo Sissoko for his part in the winner.
They struggled in the first half but stepped up after goalkeeper Cammy Bell gave them a lifeline by saving Ryan Stevenson's penalty. Kris Boyd missed a free header and forced a good save from Jamie MacDonald as Kilmarnock pressed in the final 20 minutes.
Shiels said: "To get booed off at the end is brilliant. It makes me feel so good because it's testament to how far we have come - to lose 1-0 against Hearts, and unfortunately. That's testament to the expectations of what supporters are seeing. Sometimes it's frustration and I understand it. It happens to all of us in our work and what we do."
Shiels was himself frustrated by Sissoko's failure to cut out the diagonal ball that allowed Michael Ngoo to set up Sutton for the goal.
"Everybody starts at three o'clock, he starts at 10 past," Shiels said. "He deserves criticism. He went to sleep. A lot of people said it was offside, I don't know. Maybe it was, maybe it wasn't, but they scored early and got the result."
Shiels added: "We were the better team in the second half but Hearts dug in. The shape was much better in the second half and we created chances for the forwards but we just didn't finish. We didn't get the rubs but we have gone to Tynecastle and got the rubs. In life in general you have to take defeat on the chin and realise it's not going to be your day."
Hearts manager Gary Locke was delighted to see his side secure only their second away win of the SPL season.
He said: "I thought we were on the front foot for most of the game. Coming to Rugby Park, Kilmarnock will always have a wee spell. But we defended really well and for me we thoroughly deserved the three points.
"We knew we could go two points behind Kilmarnock and they are the team we are trying to catch in seventh place."