Mixu Paatelainen felt his side deserved at least a point after watching the 2-1 defeat by Rangers at Ibrox.
Jamie Hamill's penalty cancelled out El Hadji Diouf's opener but Tim Clancy's own goal saw Killie lose the game.
The visitors thought they should have been awarded another spot-kick for Kyle Lafferty's challenge on Clancy.
"I thought so but obviously it wasn't to be," Paatelainen said. "To get one penalty, we're gracious, and to get two would have been too much."
Kilmarnock fell behind to Diouf's goal minutes before the break but got back into the game when Richard Foster was penalised for a foul on Clancy.
"I thought it was a great game," Paatelainen said. "We passed the ball well and I thought we dominated the midfield thoroughly.
"With the first goal there was a lack of communication and we lost the ball a little too easily.
"They're a quality side with quality individuals and if you're not organised and solid, or don't communicate then they'll punish you.
"We got a goal back and changed it a little bit in the second half and I thought our second-half performance was excellent.
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"It's so, so disappointing for the players to lose that goal in the end. It's a pity because our performance didn't merit a defeat."
Paatelainen praised his side's display, especially given the absence of Alexei Eremenko, Frazer Wright and Mehdi Taouil.
"I'm disappointed we didn't take anything from the game because we thoroughly deserved that," he said.
"They were a little bit fortunate in the end to get that winner but good teams are fortunate."
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