Explain the line "my body spake,not I," in "The Ballad of Father Gilligan."

Here's the context of the line you ask about from "The
Ballad of Father Gilligan," by Yeats.

The old priest Peter
Gilligan
Was weary night and day;
For half his flock were in their
beds,
Or under green sods lay.

Once, while he nodded on a
chair,
At the moth-hour of eve,
Another poor man sent for
him,
And he began to grieve.

‘I have no rest, nor joy, nor
peace,
For people die and die’;
And after cried he,
‘God forgive!
My body spake, not
I!’

He knelt, and leaning on the chair
He
prayed and fell asleep;
And the moth-hour went from the fields,
And
stars began to peep.

I've emboldened the lines you ask
about. 

Poor Father Gilligan is overworked and exhausted. 
Members of his flock are dying faster than he can get to them to comfort them and
deliver the Last Rites to them.  At the end of, apparently, another in a long series of
long days, he is dozing off in a chair when he is summoned by still another dying man. 
He reacts in a way that is really quite natural, but he sees it as a terrible
sin. 

As soon as he realizes what he has said, he begins
pleading for forgiveness.  He says that it was his tired and exhausted body that said
what he said, not his mind.  His body is tired, but his mind didn't mean what he
said.

In the poem, God seems to understand.  Even after the
exhausted priest falls asleep while he is praying for forgiveness and misses the man's
death, God sends an angel in the form of the priest to the dying man to administer the
Last Rites.