Huck acts as the go-between for Sophia Grangerford and her fiance, a Sheperdson. He delivers a note from Harney Sheperdson to Sophia and this note has information about the impending elopement that is about to take place. 

The next day Miss Sophia runs off to marry Harney Shepherdson, and the feud breaks out into a full-blown shooting match.

Huck could have deciphered the information on the note and informed Mr. Grangerford, but he fails to do so. He thinks that if he had done this, he could have helped to avoid bloodshed and the death of his new friends and adopted family. 

We see here Huck's desire to do the right thing, however, in this case as in most of the situations he finds himself in, Huck does not have a clear knowledge of what the right thing to do would be. 

If he had told Mr. Grangerford about the note, he would have been betraying Sophia's trust. Avoiding bloodshed, he would have been standing in the way of love.

Despite his regret at not helping to avoid the shootings, Huck is glad to hear that Sophia and Harney escape safely. 

"He said they got across the river and was safe. I was glad of that..."

In "The Adventures of Huckleberry Finn" why does Huck feel responsible for the carnage following Sophia's elopement?

His role in the chaos was a pretty ignorant one; he didn't know exactly what the messages between Sophia and Harney contained, but the bloodshed was so horrific that Huck narrates, "I aint' gonna tell all that happened-it would make me sick again if I was to do that.  I wished I hadn't ever come ashore that night to see such things.  I ain't ever a-going to get shut of them-lots of times I dream about them."  He regrets passing on the note, and realizes that maybe he should have "told her father about that paper and the curious way she acted."

What Huck isn't giving enought weight to is that these families have been in a feud for generations, and are always itching to find a something to shoot at each other for.  Sophia and Harney would have eloped whether Huck was there or not, and the resulting chaos was inevitable.  He gives his role in all of it too much weight, but it is understandable, since it was so traumatizing to him.  It is natural to think of the ways it might have been prevented, and this is what Huck does.