I do not think that this looks like a disease. It is possible that your blackberry plant has experienced some stress associated with transplanting. I think it's likely that it will be okay with some time and good care.
The answers to these questions might help me get a better idea of what's happening:
Has it had enough water but not too much?
What are temperatures like where you are?
Was the plant raised indoors (was it indoors at the place where you bought it?), so that it's now being exposed to more sunlight than it previously was?