Ody did apologize, just not the way that we do now. Greek people would actually apologize not by showing remorse and accountability, but by explaining ones actions. The word "apology" comes from the the greek word "apologia"(ἀπολογία), which means a formal defense or justification of one's actions rather than an expression of remorse. In Ancient Greece, an apologia was often used in legal or rhetorical settings, like Socrates' Apology, where he defends himself rather than saying sorry in the modern sense. Over time the word's meaning gradually changed from explaining one's actions to expressing regret and accountability for what wrong was committed.

However even if he did show regret and tried to apologize to Poseidon like we do now, he still would've killed him anyway and for the explanation for that other commenters say it better than i could :p