O'Neill said: "Last weekend against Everton was the first time Stiliyan has ever been left out of a 16 for a game when fit to play.
"But I have left him out in the past at Celtic - and he has always come roaring back.
"If I left him out at Celtic, it was to rest him up for big games. He has always responded - and I would expect that response again from him, knowing that he can do much better than he has done.
"He started off here like a house on fire. His debut against West Ham was as good a debut as I have seen - and trying to keep that going, with the move from one environment to the other, has been difficult.
"He is over that now. Now it is up to him, and I've got the utmost confidence he will come through this spell and show his true worth."