I know why Zod was doing it, but Superman could have moved Zod's head/wqhole away from the family without killing him. It wasn't an all or nothing thing, he was holding Zod tight enough that moving Zod's whole body shouldn't have been an issue. It may have given Zod the chance to break out and continue fighting, but I'm pretty sure at that point Superman could have taken him out without killing him. I might give Clark slack if they had shown more than just a hammy scream over Zod's death. Maybe, like someone else said, the should have had Jor-El bring up the possibility, and then have Clark think about it. Even then it probably wouldn't have been justified, but atleast it would have set up Clark eventually being haunted by what he did and realizing that he didn't have to do it, and then he'd vow to never do it again. Knowing the people behind this movie though, half of the next movie will probably be spent "justifying" what Superman did.
Honestly, the best way out of this would to have been not writing it. Its exactly the same as if Goyer had written the end of TDK Rises with Batman grabbing a pistol and shooting Bane in the head because "he had too". I honestly don't think there was ever any way to write a scene where superman had to kill Zod, or would be justified with doing it. They attempted to do that, but it didn't feel like it was his only choice at all. I think the big problem is having the next scene immediately after the death be confronting the general. They have Clark do little but angst and fight the entire movie, but we don't see any emotional scenes of him murdering a guy outside of the stupid scream right after he did it. Maybe they'll handle it in the sequel, but at this point I'd rather just skip to him being over it, and maybe having him lighten up a bit. Have him be happy in his role, put some brighter colors in the costume and just the world in general, and develop him more as a person and show some personality. Basically, make it a more hopeful movie/character. If they did that, I wouldn't really care if they glossed over Zod's death.