According to the symptoms you reported, the tissue you have damaged is probably the phrenulum. The phrenulum is a string like peace of tissue that connects the lower side of the penis head to the foreskin of the penis. It is similar and looks like the phrenulum in the mouth that connects the lower side of the tongue to the floor of the mouth. When damaged the only possible complications are bleeding and infection. If the bleeding has already stopped, adequate antiseptics would be enough. The little piece can be removed surgically, but it is not necessary.