Would straining the seeds from a blackberry puree take out some of the healthiness?

[AyaRusRowan]

I love smoothies, especially berry smoothies. When I sip a smoothie with tons of little seeds in it, however, it gives me the urge to chew it though that does very little good. I know that berries are quite good for you with antioxidants, fiber, etc. If i strained the majority of the seeds out to make the mixture smoother, how badly would it affect the nutrition of the smoothie? Would it remove a good deal of the healthy parts as well?