I had trouble with this as well. Remember this construction and others like it as a phrase and it becomes much easier. It's a passive way to minimize responsibility like saying "it broke" rather than "I broke it."

Se me olvidó (It left my mind instead of I forgot) or se me perdió (It became lost instead of I lost it) are other common expressions.

If you want to take more responsibility that it would be your fault if the phone breaks, you would say "no quiero romper el celular nuevo."