It's based on Psalm 113:9 in St. Jerome's Latin version of the Bible, the Vulgate:
'non nobis Domine non nobis sed nomini tuo da gloriam'
The corresponding verse in the King James Version is Psalm 115:1
'Not unto us, O LORD, not unto us, but unto thy name give glory, for thy mercy, and for thy truth's sake.'
The film version is by Patrick Doyle who composed the music and rearranged the words slightly. I believe Patrick Doyle's voice is also on the soundtrack. Note that 'nomini' has been changed to 'nomine' but that doesn't affect the meaning. They are alternative versions of the dative case in the third declension.
The words in the film version are:
Non nobis Domine Domine
Non nobis Domine
Sed nomine sed nomine
Tuo da gloriam
I would translate that as:
Not to us, O Lord, O Lord,
Not to us, O Lord,
But to your name, but to your name
Give glory.