The movie's message -- not everyone is a winner
Movies tend to focus on the guys who win, the rags-to-riches stories, the guys who walk away at the end with the pretty girl, the heroes who get revenge, the lawyers who deliver justice, the cops who take down the bad guy, the boxers who win the championship.
But this movie serves as a reminder that not everyone wins; not everyone makes it in life.
In other words ---- what happens to those guys who lose the fight, what happens to those people who don't get excellent grades and become ivy leaguers, what happens to those people who never get rich and famous, what happens to the guys who fail to make the team, what happens to those people who don't get to marry the beautiful princess?
Whereas Rocky Balboa is a rare, one-in-a-million case of the guy who does manage to win the fight, this film pushes us to recognize and acknowledge the guy who loses the fight (i.e Tully).