near accident who's fault is it?

I had a near accident on mini roundabout. this roundabout is on the road I was entering from small road going left.I looked to the right and car was indicating left so turning in the road I was coming out from, so I came out as well.so me and car on the right kind of turned same time. car behind that first car from right then was going straight and came out really fast and nearly hit me. I was already nearly fully on the road. we stopped at same car park and they were blaming me not giving way to vehicle from right. I said first car was not coming my way he turned and if he waited and didn't pull around that car he would have seen me. but they were like no you just look for all the cars from right not just first.
Is it my fault at all? I was very upset. I am the new driver but very responsible and always drive according to rules