Ranieri visits his former employers Chelsea on Sunday, and the Italian is demanding more of his player.
Cairney picked up an ankle injury on his third Premier League appearance and is yet to score a goal this season but has been moved into a more advanced role by new Cottagers boss Ranieri.
"He is a good player with a high quality, but I want more from him," Ranieri told 'Sky Sports'.
"I want him to play as well in the Premier League as he did in the Championship. He scored a lot of goals there, and I want the same again.
"He makes assists but also he can score goals, these are important because he has very good timings to arrive, he has a good left foot and I say to him, 'try, try', but, it's a little hard."
"He has to shoot more; he has the quality to shoot, he must improve," Ranieri added.
"Try! It's no problem, try! I ask him during training, 'shoot at goal, shoot at goal', but he passes and he passes.
"Maybe when he comes to me on the bench he will realise and say, 'maybe it's much better if I shoot at goal'."