All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
You are not sinful for what happened, as Allah says (what means): {And there is no blame upon you for that in which you have erred but [only for] what your hearts intended.} [Quran 33:5] Ibn Katheer said, “The sin is on the person who deliberately does something wrong.”
A person who deliberately kills an animal without reason is the one to be blamed. ‘Abdullah ibn ‘Amr narrated, “The Prophet said, ‘Whoever kills a bird without right, Allah will ask him about it on the Day of Judgment.’” [Ahmad, an-Nasa’i and ad-Darimi]
Therefore, you are not Islamically required to give charity for killing a pigeon because there is no text in the Sharia that stipulates that the killer of an animal must give a charity or expiation, with the exception of what is mentioned regarding a person who assumed Ihraam (state of ritual consecration) for Hajj or ‘Umrah if he deliberately kills a game (hunting), as there is a punishment for it in the Sharia.
Allah knows best.