In Judaism, there is a specific way of slaughtering animals, known as Shechita, in which the animal is slaughtered with a sharp knife by cutting the throat and the blood is drained completely on the ground.
The reason for slaughtering animals in this specific method is to give minimum pain to the animal and not to eat the blood, as the life of animal is in the blood(Deut. 12:23).
Christians are free from Jewish Laws and Traditions. We follow the New Testament, and as the name itself implies, it is a New Covenant and the Old Covenant is no longer needed. The New Testament also has few laws, mostly related to morality, Christian way of living and ordinances in the church.
The Council of Jerusalem (Acts 15) was for the Gentile believers in Antioch, Syria and Cilicia. The letter as in Acts 15:23-29 (NIV),
The apostles and elders, your brothers,
To the Gentile believers in Antioch, Syria and Cilicia:
We have heard that some went out from us without our authorization and
disturbed you, troubling your minds by what they said. So we all
agreed to choose some men and send them to you with our dear friends
Barnabas and Paul— men who have risked their lives for the name of our
Lord Jesus Christ. Therefore we are sending Judas and Silas to confirm
by word of mouth what we are writing. It seemed good to the Holy
Spirit and to us not to burden you with anything beyond the following
requirements: You are to abstain from food sacrificed to idols, from
blood, from the meat of strangled animals and from sexual immorality.
You will do well to avoid these things.
The reason for the Council in Jerusalem was to unite Jews and Gentiles in the church. Though the Gentiles were freed from circumcision and other laws, the most important part of the Dietary law, Shechita(slaughtering method) was given to them so that Jews and Gentiles can dine together. The law was mainly in favor of the Jews, not for the Gentiles.
Paul himself delivered the message of the Council of Jerusalem to Antioch, Syria and Cilicia. However, Paul never never imposed Jewish Laws to the Gentiles unnecessarily.
Therefore do not let anyone judge you by what you eat or drink, or
with regard to a religious festival, a New Moon celebration or a
Sabbath day. (Colossians 2:16, NIV)
Paul also encouraged Gentile Christians to live in peace with the Jewish Christians. Paul suggested that gentiles should not eat defiled foods in the presence of the Jews, such as foods offered to idols and animals not slaughtered according to Shechita law, so that they both may come together and worship together.
Therefore, if what I eat causes my brother or sister to fall into sin,
I will never eat meat again, so that I will not cause them to fall. (1
Corinthians 8:13, NIV)