I don't know that it is necessary for losers to shake hands in order to be called "good sports". But here are some behaviors that don't qualify.
- Picking a fight with the winner
- Trashing their equipment or facility.
- Thowing at batters when the loss becomes evident
- Disparaging the winner's character, social or financial circumstances, looks or parentage.
- Accusing the winners or umpires of cheating
I think it is pretty important that teams don't engage in these behaviors, even though they "don't like losing".
Being a good sport lies somewhere between these egregious examples and offering to buy the winners ice cream.
Put simply, a good sport is respectful of the winning team (and when the shoe is on the other foot, respectful of the losing team.) Just like doffing your hat at a funeral, if the social norms say that not shaking hands is disrespectful, then shake hands.
Locally, high school players line past each other, tapping hands. It's not always polite, but that's not obvious to the spectators.