Robbie Keane's Hoops debut ended in disappointment as the Tottenham player was denied by a series of fine saves from Killie keeper Cammy Bell.
Hoops boss Tony Mowbray: "It's not the result we wanted. We needed to hit the ground running with the new signings, but it didn't quite happen tonight.
"We didn't put the ball in the net. We had enough of the ball in their final third, but we didn't put the ball way and they defended really well.
"But that's football - we had enough opportunities to win the game, we didn't take them and we lost the game ultimately.
"But you take it on the chin and move on.
"We have a game at the weekend and we keep going.
"We're trying to build a team that can win football matches week in week out and be successful both domestically and in Europe.
"We have enough talent on the pitch to do that."