I would think you'd want to be saying something like
thank you for the letter blahblah. I'm sure that it contributed to the quality? of my application. Unfortunately I was not accepted this time, but I intend to spend this year improving my qualifications/applications so that I can be more successful next year. I hope that you will consider writing another letter next time, will be in touch, blahblah.
That way you're appreciating their letters and putting the responsibility for everything on the overall application, not the letters.