The end shade of naturally dyed items is determined by many variables:
- what kind of fibre content the item is (ie, if your item has some synthetic content, it will result in a paler shade, and silk and wool tend to come out darker than plant fibres like cotton
- if the item is old or new (something that has been washed  a lot of times will take the dye more readily as the fibres will have begun to break down somewhat, and so the dye can penetrate very easily)
- whether it has sizing on it (many things, especially garments and housewares like napkins, are coated in a type of chemical sizing to resist staining - unfortunately this also has the effect of resisting the dye somewhat).  If you're aiming for dark shades, and your items are brand new, you definitely want to wash your things very very well before dyeing them - I would run them through the machine more than once even
When using an indigo vat, you build your colour up through repeated dips - so for darker shades you need to dip many times - as many as 10 or more.
With other natural dyes, for darker shades, you need to use more dye.