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I replace my heater core recently and I had coolant under the front seats carpet, but it didn't make to the back....I guess I was lucky.
Did you wipe under the floor carpet when you replaced the heater core? when you replace the core you are already pulling the mat back so it is convenient.
Removing the coolant from the carpet itself (soaked) is a different story. What I did is suck it with paper towels (rub the carpet with them)...I used a whole roll to get the bulk of it. Then I put a couple layers of paper towels over the carpet and put weight on top to make sure they sucked more coolant. It worked pretty well and left it almost dry.
I finished by pouring some carpet cleaning powder and taking the car to a car wash place with a powerfull vacum cleaner. Don't do this with your vacum cleaner as the wet powder can clog it.

Klaus method is probably the best, but I didn't feel like removing seats etc.