More than anything the end of Rocky illustrates that Rocky has "gone the distance" (all 15 rounds of the fight). That's all he wanted. He didn't care if he lost, (which he did. Apollo is the victor by points in this match) only that he didn't loose by knock-out. He is elated that he "went the distance" and proved to Adrian that he had what it takes to go the distance. He's looking for Adrian because he want to celebrate this victory with her. Nothing else is important. This is why he doesn't care about having a rematch. He was never interested in winning the fight. He was only interested in "not being another bum from the neighbor hood".
The need for "going the distance" as the main goal for Rocky as the protagonist is exposed in the lyrics to the theme song (albeit Rocky III) Eye of the Tiger by Survivor
Went the distance, now I'm back on my feet Just a man and his will to survive
and in a monologue he delivers to Adrian:
Ah come on, Adrian, it's true. I was nobody. But that don't matter either, you know? 'Cause I was thinkin', it really don't matter if I lose this fight. It really don't matter if this guy opens my head, either. 'Cause all I wanna do is go the distance. Nobody's ever gone the distance with Creed, and if I can go that distance, you see, and that bell rings and I'm still standin', I'm gonna know for the first time in my life, see, that I weren't just another bum from the neighborhood.
This monologue sets up the meaning of the end of the movie. The movie ends with the most important moment of Rockys life. Rocky is on top, because he's gone the distance and proven that he was not just another bum from the neighborhood.
