No, don't start trying to make a "ramp" of concrete. Chances are it won't come out very even anyway.
Johnsonite has a floor leveler system that consists of 4 foot long 1 foot wide strips of hard PVC plastic. These strips vary in thickness across their width and they come in all different combinations of sizes so that you can stack them up or spread them out so that you have anything from a 3/4 inch rise over one foot to a 3/4 inch rise over three feet.
Phone up any carpet retailer and ask for the "Installations Manager". Ask the Installations Manager who sells flooring installation supplies in your area. Any place that sells flooring installation supplies can order these leveling strips for you. (Tell the installations manager you're interested in finding places that "bind" carpet edges to make an area rug out of piece of scrap carpet you have. If he knows you want to buy these leveling strips, he'll probably want you to go through him, and that's gonna raise the price.
You just glue or nail down these leveling strips.
Johnsonite LS-40 Leveler Strip, 1/4" to 0"