It's not what we give up, but what we give.
It is our love that God desires - not the sacrifice.
The old habits and behaviors that we forsake may indeed feel like sacrifice if we have not surrendered to the Holy Spirit. When we allow the Holy Spirit sanctify our hearts, He fills us with the desire to please Him.
We no longer think about our lives as a list of things we have, can, or will give up. We keep adding to the list of the things we want to do for Him - not keep a record of the things we have given up because of Him.