How can I reduce the heat loss through floor?
Not sure if this should be a comment or an answer. You will need something on top of the concrete but under the radiant tubing to reflect the heat upward. They do make a metal coated wood for that purpose that has channels already routed out for the tubing. It will ad to the height of your new finished floor.

I assume your concrete is on top of earth or soil and no way to get under it. ( my forth floor condo has a two inch concrete floor so i could in theory put something under it.) You will not be able to stop the concrete from absorbing some heat but once the concrete has heated up it will act like a big heat sink and radiant that heat back out. that said it might be that the reflective material on top of the concrete would prevent the concrete heat sink from radiating upwards.