Contrary to popular belief, people with Asperger's do have empathy. They care about how others are thinking and feeling but they often have difficulty putting themselves in other people's shoes. This is a skill that can be learned over time..
Trouble picking up how others are thinking or feeling via tone of voice or body language can make people with Asperger's appear less than empathetic when they don't mean to be.
The autism community talks about the double bind empathy problem. This is where neurotypicals can seem less than empathetic - by failing to take into account how people with autism see the world. They might ignore the fact that autistic people have a tendency to take things literally, asking someone to take a seat rather than sit down.