Back Pain On Road Bike

Hello group, I have been riding a Mountain bike for about 3 years now.

I decided that I want to get a raod bike so I borrowed my mates for about 3
weeks now.
Its the right size for me.
But I find it very uncomfortable, and I get a sore back, where on the
mountain bike I did not get any back pain.

Is this normal, and will I get used to it ?

I am not sure if I should go and buy a road bike if I will always get back
pain, but like anything, maybe this is normal, and I will get used to it.
Am I right ?

Thanks for any feedback.
Bill