If I can't get my tongue around it, is it a terrible thing if I'm only able to say the sound in the "English" way?
It's not terrible, of course, but it's not good. You won't be able to distinguish between hard and soft "r". Then, especially if your accent is non-rhotic, the sound may desappear because English "r" is less audible than Russian, isn't it? Alveolar trill is a really difficult sound. Children fight against it for a long time (I couldn't pronounce it untill I was seven years old). Soft "r" was a little bit easier to me: I started pronouncing it a year before. I managed to pronounce hard "l" only at nine. Soft "l" did noy cause any problems to me.