Yes, you can loose some nutrients by juicing.
But if you look at the amount of whole foods you put into juice and relate it to amount of whole foods you put into blender it is still extremely better to do the first one. ( under certain conditions : juice at the first stage of raw/vegan or after leaving the SAD to make an easy access for nutrients entering your body and as Steve says -- > juice from time to time, to not overdo the sugars ).
Regarding your sickness from spinach, celery, cucumber, banana, mango and lime juice :
- try to skip the banana ( maybe to heavy )
-add some cayenne pepper for easier digestion
-add some honey ( if you allow yourself ) for additional enzymes
And smile!