As distressing as the event was, you need to accept that we cannot control events.
What you can do is to decide to accept the event for what it is and, at best, perhaps decide what you might do the next time there is a pigeon's baby on your balcony . . . perhaps, you can discourage pigeons from coming to your balcony; perhaps you can decide if there is a pigeon's nest there, you will not clean the balcony until the little birds have flown away . . . .
I know that you would want to save them, but you couldn't . . . you need to tell yourself that you will learn from this, plan what might be a good plan for you if the event happens again, and go on . . . .I know that this is not the best solution for you because you would want to undo what has already happened, but we cannot . . . I don't know if this helps, but try it and let us know how you are doing . . .KC