The main antagonist is arguably the state itself, the government's behavioral modification program. The film, of course, makes Patrick Magee's Mr. Alexander a more visceral opponent later on, but Burgess's novel complicates that. The true villain is the philosophy that destroys Alex's capacity for choice, even his capacity for evil, replacing one monstrous form of control with another that's dressed up in clinical, moralistic language. That's the real horror.
The 'Ludovico Technique' is the antagonist. It's not a person; it's a process, an idea made flesh through aversion therapy. It reduces Alex to a clockwork orange—organic on the outside, mechanically predictable within. Even characters like the Minister of the Interior or Dr. Brodsky are just agents of this systemic evil. The story’s tension comes from watching a brutal individual be broken by a brutal system, leaving you wondering which is worse. The ending, especially the restored 21st chapter in the book, drives that home harder, suggesting the true defeat of the antagonist might be Alex's own, sad maturation, which the state never intended.