No, certainly not in American English; that would sound weird. Common responses to "Thank you very much" in the States include "You're welcome." "No problem." In the South: "You bet." There are many other phrases used, also, but "It doesn't matter" sounds like you are blowing the person off (do not value their thanks).

Use "it doesn't matter" or "it's no problem" or "it's OK" if YOU made the effort. "No problem at all!" :D In some contexts, you'd be saying that the effort is worthless.