Well, I don't know if you're looking for something short or not, but from what I've seen the only anime that come to mind are Yu-Gi-Oh! ZEXAL, the protagonist Tsukumo Yuuma can be described as a loser since he loses a lot of his Duels, fails at a lot of his "Kattobingu Challenges", and is kinda picked on a lot by his peers. Also, My Hero Academia since Midoriya or Deku has no quirk in the beginning and is kinda spineless and he's also bullied by Bakugo and the other students.