The question that comes to mind when reading this verse, "is thanksgiving a sacrifice?" I suppose when i think of sacrifice I think of giving something up; you know, like I had to sacrifice my vacation savings for that emergency room visit. Is that the right attitude to have while giving thanks; Ah man, do I have to give God thanks? Do you know how wrong that sounds? Unfortunately that may be our attitude when it comes to giving thanks if we are prideful. When the idea of giving accolades to anyone but ourselves seems wrong, then thanksgiving will be a sacrifice.
The word sacrifice here doesn't have the more modern sense of giving something up. A sacrifice in Judaism was required, it was giving God what he was due, and it pleased God to receive such a sacrifice. When a Jew thought of giving a sacrifice he didn't think he was giving up anything, he was rendering his due service to God. We should give thanks because it would be unusual not to, thanksgiving is a natural result of gratitude, and it pleases God when we display our gratitude to him. So, if you don't have anything else to offer God, give him your thanks!
May God bless you