Offhand I can think of two sports movies where the protagonists don’t win the big competition at the end of the movie: The Bad News Bears and Rocky.
What are some other examples?
Thought of another one: Tin Cup.
Bring it On.
A League of Their Own (well, most of the protagonists lose).
How about this one, 15th of 16 
Friday Night Lights? I know they changed stuff from the book (where they lost in the semi-finals rather than going to the finals) but I think they still didn’t win state in the movie.
Cool Runnings.
Rocky.
Coach Carter
Rocky Balboa.
Beer League comes to mind.
Kingpin.
I’ve noticed that sports movies are the one place where it is “safe” to show the protagonists losing in the climax and not have it be considered a tragedy. Possibly a cathartic metaphor for the inevitable losses in life.
I was going to answer Victory (or Escape to Victory), but apparently I didn’t remember the end of the movie correctly. The POWs don’t lose to the Germans, they tie them. But the POWs do win a larger battle in the end.
IIRC, The Indians win a playoff game at the end of Major League but go on to lose the Series.
That’s sort of correct. The movie ends when they win the one-game playoff, but in the sequel, it’s mentioned that they lost in the ALCS afterwards.
Real Steel.
Charlie Brown’s All-Stars.
Lucas