Analogy: a story of death and guilty feelings
There was one announcement-only email list posting after a boy at school collapsed on the baseball field. He had no breathing and no pulse, and the coaches did CPR until the ambulance came but it wasn't enough. The boy ended dead, and the coaches felt like they had shown a terrible failing of love.
There were some things I really wished to tell them, but I couldn't through lack of contact details.
First of all, CPR is premature and inappropriate until a patient is clinically and legally dead. The boy did not die on the ambulance or in the ER; he died on the baseball field before the coaches began CPR. The marketing slogan "CPR saves lives" fundamentally misportrays details; even at its best, CPR is 35% as effective as a beating heart, and all it does is hold onto a very slender chance that the ER can get a patient back ("résuscitation" in French means "resurrection [from the dead]"). It's worth doing but the odds are slender. Which leads me into my second point:
Second, even under optimal conditions the percentage of patients who are successfully brought back to life after a first responder does CPR is less than 10%. No matter how well you do, it is more than 90% likely that it won't do any good. Now it's worth doing; I don't want to discourage people from doing CPR. But please don't expect that if you care enough and do a good enough job you'll get the person back. 90+% of the time, it doesn't matter how much you care or how well you execute; it won't help.
Third, perfect CPR doesn't happen. This point was specifically made in an Emergency Medical Technician class I took. Something always goes wrong, and that's normal. The teacher's beating the drum of "Perfect CPR doesn't happen" was not teaching the general public who may perform CPR off of training from years back. The teacher was directly telling students who would become EMT's and usually paramedics, who would be thoroughly trained in CPR, with ongoing professional development and probably perform CPR on some kind of regular basis, that perfect CPR doesn't happen; it's a chimera and even if it's your job to do CPR, you're going to make mistakes again and again - and we should make our peace with it instead of expecting perfection. (And I am almost positive the coaches screwed up in some detail small or large, with timing off or something like that.)
Fourth, I am positive the coaches would have given their lives for that boy if they saw any way to do so, and would have done so in a heartbeat. They felt guilty that the boy's death showed somehow that they didn't love him enough, because if they had loved him enough he would have come out of the ER alive. This may or may not be rational, but these kinds of sentiments somehow seem to hover in a situation like theirs—or yours.
What you can take away - and what you can all do
The OP feels that management should have done something they didn't do. Well, um, maybe. I make enough clumsy mistakes when I am not under any particular stress, and I'm sure that management did something wrong, or didn't do something helpful that you could have done. You could spend the rest of your life Monday morning quarterbacking on that one. However, you did the best you could think of in a situation where you and others were stunned and reeling. You were acting in grief, and you should have done so.
About next steps from now, other people have mentioned a grief counselor. I might suggest you consider collaborating with the employee's family and set to work on some community service project or undertaking where all those connected with him (and not just the many people at work) could work together to undertake a community service project in his honor. And go ahead, putting grieving connections in a place to erect a monument of service.
And one last thought. Some people have said that people who are grieving do very well with a puppy or other pet. Sometimes even just going to a good pet shelter and spending some of the time with the animals there can be good—and not just because you might take a rescue pet home. As a rule, most pet shelters could use more time with strangers coming in and giving a bit of attention to what are often very sweet animals.
Just a few thoughts.