Sympathy and compassion are related to empathy, but all three are slightly different.
Sympathy is feeling for someone but not sharing in the emotional connection. Sympathy tends to look for the silver lining.
Compassion is sympathy and the want to do something to fix the situation.
In addition, the opposite of empathy is shame. Shame is associated with feelings such as humiliation, guilt, or unworthiness. By practicing empathy and connecting with the underlying emotions that someone is experiencing, you are conveying the message that their emotions are okay. If you choose to shame someone for their emotions, you are telling them that their emotions are not okay, and you are only furthering their feeling of shame. If someone makes a mistake, try asking yourself "Why would they make that mistake, maybe something is going on?", instead of saying to them "I can't believe you made that mistake!" That is practicing empathy.