I would also make the case that this is a Superman who hasn't had any experience with bombs. It's one thing to notice sounds or anything, it's another thing to know what they are. Now, I get that this isn't going to change your mind, but this is one of the reasons I don't mind it. Now on the other hand, I would never want someone to be able to pull the same stunt on this version of the character ever again. Now he would not only be more aware, but he would recognize certain sounds or anything, that he remembers from this incident (and I expect this incident would be tattooed on his brain now, considering it's an awful thing and it really did disturb him).
I feel this one, to an extent. I agree with you that we didn't get enough access to him as a character in this movie. I would have liked to get into his head a little bit more, to see him interacting with people. I think it's the fact that he's so stoic that makes a lot of viewers feel that he's aloof. Like, we see how much he truly does care, but we rarely hear him say it, except to Lois.
With that said, having been somebody who was a manager and had his decisions questioned a lot, I think having a character like Superman feel it necessary to explain himself to anybody, could just be perceived as weakness in the eyes of his detractors, because it puts him on the defensive. The only time you really want to see Superman on the defensive is when he's defending somebody else. But I realize that's just my opinion, formed due to my personal experience of what happens when I try to explain myself to people.
The only way he could have tried to save anybody is if he'd had more time to react, or if they slowed time down, but again, all of that would negate the drama of the moment, which is meant to be a total shock. I thought he looked pretty upset, though, and as others have pointed out, he is them shown on Lois' hotel balcony talking about how upset with himself he is that he didn't see it.