The original question had to be edited. I think that the frog's reaction is deliberate upon experiencing the death of the nightingale. He spins it, almost blaming her for her own death. In the process, the frog's reaction is to extol his own "guidance" of her:
"I tried to teach her,
But she was a stupid creature -
Far too nervous, far too tense.
Far too prone to influence.
Well, poor bird - she should have known
That your song must be your own.
The real cruelty of the frog is on stage at this moment. The frog understands that her presence threatened his stature in the bog. He could not compete and the only thing he could do was to eliminate the competition. He did so in the form of a mentor and a teacher. In the end, when the nightingale died, the frog is pleased that he is able to "own his song" and sing away in the bog. The frog's reaction is a brutal reminder of how some take advantage of others and how being too trusting can have disastrous effects. It is here in which the frog's reaction is significant for it fits his characterization.