Congrats to Rosberg. No, he doesn't have Hamilton's natural ability, but he won the championship (just like his dad did) in the only way possible: by being consistent, and capitalizing on his teammate's misfortune and mistakes.
I don't think that devalues his achievement in any way. Everybody knows that Hamilton has him beat any old day of the week, all things being equal. So you have to respect how he managed to keep it together all year long to finally bag the title.
While 2015 was pretty much a walkover for Hamilton, 2014 went down the wire and it was Rosberg's bad luck in the final race that decided the outcome. So I don't think anybody can honestly say he doesn't deserve it.
Hamilton has nothing to feel bad about, really. He broke all kinds of records this year, and his status as one of the greats is undisputed.