First, take note of the wording: "...give thanks FOR everything..." (emphasis added!) My point? Too often we think we should thank the Lord "in everything" and assume He doesn't expect us to be thankful "for" all that happens. However, Paul clearly uses the wording, "for everything." What was his point? Everything that God allows in our lives will eventually be used for His glory and our good, Romans 8:28. We need to see things through God's eyes.
Second, not only is singing a sign of the Spirit's filling, but also is thanksgiving. A truly Spirit-filled Christian will be a thankful Christian. A believer will see that God is working in our lives and uses everything to accomplish His will in us and through us. And let's remember that expecting God to fulfill His will in our lives is not for our benefit as much as it is for His benefit.
We thank the Father. Remember chapter one and verse 3, "All praise to God, the Father of our Lord Jesus Christ, who has blessed us with every spiritual blessing..." God the Father made sure we would have everything we needed to live a victorious life for Him. And it is to Him that we show our appreciation.