To the contrary, narcissists do have emotions, what they lack is empathy and tend to be very emotional and needing to be the center of attention and like to emotionally manipulate others for their own gains. Most narcissists learn how to praise enough to get others to believe they actually care, but they really don't care, they just like to have people around them that they can control and tend to like to keep their flying monkeys to help them get what they want.

A psychopath told me in confidence that they find narcissists very useful and easily manipulated and when they are finished with them, they take extra pleasure in bursting their bubble and casting them aside.

A lot of people get confused about narcissists however because if they see "some" selfishness in a person they automatically think the person must be a narcissist. That is not advisable as there is "some" narcissism in each person and often it's on a spectrum where some may have more but not quite be a person with NPD.

There is also somewhat of a spectrum when it comes to a person having empathy as well. Some can have empathy but also be selfish, and some may have too much empathy where they give too much to others and not enough to themselves.