In English, "thanks anyway" is a common way of acknowledging the other person's effort/attention even though the end result wasn't satisfactory to the person doing the thanking.
Thankee: Here, have a piece of cake that I made. Thanker: I'm afraid this cake isn't really edible at this point in time. throws cake in the bin Thanks anyway (for the effort in making the cake).
Thanker: Hi, I would like to buy your Item X but only if it comes with Item Y. Do you have Item Y as well Item X? Thankee: Sorry, we don't have Item Y in stock at the moment. Thanker: Damn it. Thanks anyway (for checking for me).
Is there a Japanese equivalent? The closest I can find is でも、ありがとう but that's not as succinct as "thanks anyway" because I have to insert a sentence before it (I'm afraid this cake isn't really edible. でも、ありがとう).