What is important about David's response to the man was the condition of David's heart. David knew the value of the sacrifice to God and to himself. He knew if he offered a sacrifice to God that didn't cost him anything, then it wasn't really a sacrifice. David would have given up nothing out of his own time, money, and resources; the offering would have no meaning. The meaning was so important that David insisted on it costing him, as David wanted to be the one to make the sacrifice.
Today, you and I don't offer burnt offerings (sin offerings) up to God. Jesus Christ was that burnt offering, or sacrificial sin offering. Jesus suffered on the cross, not because He was excited to do it, but to end anyone having to make a sin offering. If Jesus was the final offering for our sins, then how do we offer up to God a sacrifice that costs us something? How do we make sure our hearts are like David's?
In Hebrews 13:15, the scripture says we should continually offer up to God the sacrifice of praise. The sacrifice of praise, in this instance, is an actual utterance from our lips and takes the place of us having to make a sin offering. Yes, there are other forms of praise to the Lord, but specifically, it is talking about what comes out of our mouths to praise and glorify Him. That praise, in this verse, is a direct response to God having already forgiven our sins. It is praise for Him and His amazing work in our lives that He completed 2,000 years ago on the cross.
You may not feel like praising the Lord at every given instant of the day, but I am confident you have done enough sinning to require a burnt offering every instant of the day. Every moment of the day is a chance to praise and thank God, with your lips, for the sacrificial offering of Jesus on the cross for the forgiveness of your sins. Do it in remembrance of Jesus' sacrifice on the cross for your own personal salvation.
And if you have no other thing to praise the Lord for, do it because it will bring Him honor, even if you are not excited to do it. If you still can't think of anything in your current situation to praise Him for, do it anyway. It's a sacrifice because He deserves it even when you don't feel like it. It's OK if it costs you something.
Don't take my word for it; look it up: 2 Chron 24:24, Ps 34:1, Ps 54:6, Ps 148, Luke 7:36-43