Psalm 69:30-31 I will praise the name of God with a song, and will magnify him with thanksgiving. This also shall please the LORD better than an ox or bullock that hath horns and hoofs.
There is ample biblical evidence (including this verse) that clearly indicates the physical sacrifices offered in the OT were for the very same purpose that spiritual sacrifices are prescribed in the NT – as an expression of gratitude for forgiveness already rendered by God, not a means of obtaining such forgiveness from Him. (Otherwise, why would they show up in the millennial kingdom? Ezekiel 40-48; Zechariah 14:21.
Apparently, what really mattered to the Lord was not the animal that was sacrificed (though there were certainly criteria these animals had to meet, which mainly served as a picture of the sinless Lamb of God, John 1:29; 1 Peter 1:18-19) but the heart condition of the one bringing the offering and the motivation behind it.
Psalm 51:16-17 For thou desirest not sacrifice; else would I give it: thou delightest not in burnt offering. The sacrifices of God are a broken spirit: a broken and a contrite heart, O God, thou wilt not despise.
On a practical level, let's remember that God is pleased when we express our gratitude and give thanks for the blessings He has bestowed upon us. Forgiveness (Psalm 32:1-5). Provision (Philippians 4:19). Healing (Psalm 103:3). Answered prayer (Matthew 7:7-8; James 5:16). Truth (John 17:17). Purpose (Revelation 4:11). Eternal life (John 10:27). Abundant life (John 10:10). Assurance (1 John 5:13). Confidence (2 Corinthians 5:8; Hebrews 10:35). Love (Romans 5:5). Comfort (2 Corinthians 1:3-4). Peace (John 14:27). Power (Ephesians 3:16). Victory (1 Corinthians 15:57; 1 John 5:4). Hope (Hebrews 6:18-19).
And the list could go on and on...
Hebrews 13:15 By him therefore let us offer the sacrifice of praise to God continually, that is, the fruit of our lips giving thanks to his name.
Psalm 103:1-2 Bless the LORD, O my soul: and all that is within me, bless his holy name. Bless the LORD, O my soul, and forget not all his benefits: