Dywedodd Ms Griffiths, oherwydd bod Cymru gyfan yn derbyn un ffurf neu'i gilydd o gyllid strwythurol, mae'r wlad yn methu o ran ffrydiau cyllid Ewropeaidd eraill sydd ar gael.
Hawarden Community Council in Flintshire had said Hen Wlad Fy Nhadau would not be played there on Sunday "out of respect" to the anthem because villagers did not know the words.