Dead animal smells are just nasty and sickening, even if they're produced by smaller animals like rats. Yes, it's a natural by-product of the natural cycle that helps keep humans away from a decaying, possibly disease-infested object, but it's hard to think of the wonders of nature when the smell hangs around. There are a couple of solutions that you can try on your own before resorting to the expense of a professional.
Fill a shallow bowl with baking soda--an alkaline and chemical base substance, that will balance with an acid base substance. Place it on one side of the room, to the right or to the left of the smell's source.
Fill another shallow bowl with vinegar, the acidic substance to work with the alkaline base of baking soda. Place this bowl on the opposite side of the room from the baking soda, so that the origin point of the odour is between the vinegar and the baking soda.
Soak a cotton ball in vanilla extract and place it on the surface of the baking soda. Putting these three materials in this proximity could neutralise the pervasive smell.
Run an electric air cleaning machine in the area, one that included a filter made of silica gel or activated charcoal, to help absorb the offending odour.
Drill into a wall or other part of a building a hole large enough to insert a neutralising agent or disinfectant product inside the structural element.
Spray the inside of the hollow space in all directions, if this is the type of product that you're using.
Cover all of the drilled holes with electrical tape, with or without cardboard or wooden covers between the holes and the wall, as well as closing off any other cracks, to keep the odour and the odour-killing product inside the trapped space.
Plug in a fan and point it toward an exit, a door or a window, to better move the smell away from its origin point.
Keep in mind that the smell will go away on its own once the source has completely dried out, although it's also understandable if you don't want to wait the days or weeks for this to happen.
Simply masking the odour with a general air freshening product is going to do just that--mask the odour but not get rid of it.