Actually, it's human nature to be jealous. If you would never feel jealousy, you wouldn't be able to hold on to the one you love. However, it's acting on this jealousy that could form a problem.
If she left you because of your jealous behaviour, you should probably find someone to talk to about these feelings.
Being in a relationship can be hard when you're easily made jealous, not only for her but for you as well. It's worth it to find help.
Don't think being jealous has anything to do with loving a woman less. It's love that makes us jealous. It's one of those tragic situations where you love her and the consequences of that love drive her away. You should try and get a hold of your jealousy so you can learn to let go and have a happy relationship.