As mentioned in the comments, the movie's themes are explored and contrasted in some detail in this wiki. Some viewers focus on certain aspects of the plot while others prefer other aspects. In light of the title of the film, the following critiques are probably good summaries of what you could interpret from this Cormac McCarthy story:
William J. Devlin analyzes the opening narrative of "the traditional western hero portrayed by Sheriff Ed Tom Bell. Bell relates the following about himself and his life in the West: 'I was sheriff of this county when I was twenty five [years old]. Hard to believe. Grandfather was a lawman. Father too ... You can't help but compare yourself against the old-timers. Can't help but wonder how they would've operated these times.' Here, Bell acknowledges that he is part of a tradition – and not simply that of generations of lawmen in his family ...
But it is now 1980, and times have changed in at least three significant ways. First, the western frontier is no longer characterized as the 'Wild West,' where the land is unpopulated and unsettled, power-hungry tycoons dominate the innocent, and legal order is yet to be established. Second, though the 'Wild West' has been 'tamed' in one respect, the modern West has a new breed of lawlessness, [where] Bell explains in his opening narrative '... The crime you see now, it's hard to even take its measure.' ... Third, the hero of the West has grown old. Bell is no longer a young, twenty-five-years-old sheriff, ready and willing to act accordingly to his moral duties ... Instead, he is now weary and cautious: '... But I don't want to push my chips forward and go out and meet something I don't understand. A man would have to put his soul at hazard.' ...
Though the western frontier has been tamed so that towns have been settled and cities have developed, a new kind of wildness has now spread and ravaged the world. Bell, part of the tradition of the 'old-timers' ... is confused as to how to handle this new immoral wildfire."
William Luhr focuses on the experiences of the retiring lawman played by Tommy Lee Jones at the beginning of the film. "[He] feels that the evil surrounding him has metastasized beyond his comprehension and that he can no longer even pretend that he can deal productively with it," he said. "On one level, such comments reflect anxieties shared by many older people who feel that their world is passing them by, that the securities upon which they have built their lives are becoming ignored or invalidated. But [David Fincher's 1995 film] Seven, No Country for Old Men and other recent neo-noirs indicate that more is involved, that a new era of evil is emerging. Such films partake of a millennial sensibility, a sense that the world is entering a phase so degenerate that traditional agents of law, stability, and continuity can no longer cope with, or even understand, it. Such films offer no hope for a viable future, only the remote possibility of individual detachment from it all."
FYI, The Road was also based on a Cormac McCarthy novel. He's not what one would term a happy writer and tends to (bleakly) explore themes like fate, morality, and the human psyche.