Precisely speaking, to be moved by something is to have it emotionally deeply affect you with compassion/sympathy, as explained on Dictionary.com. That something is usually an action that represents the manifestation/violation of crucial moral standards. It can have a positive or negative connotation. Usually (not always), there is compassion directed to a person involved. I can be moved by someone’s desire to help others before helping themselves, similarly, a tragedy or a violent crime against someone can move me with compassionare emotions towards the victims.
In your situation the underdog situation and the perseverence of the Croatian players against the odds is enough to instigate strong compassion, to move you.
In short, it can be used positive and negatively, as long as the feelings are deep and compassionate (sympathetic)