Whenever this happens to someone it's always a horrible feeling where one feels very guilty and ashamed no matter what people say to you and unfortunately mistakes like these are almost the bread and butter of any extremely experienced grey beard so it's kind of normal that something like this happens to someone at some point sooner or later. The only people who never make costly mistakes are those who were never trusted with responsibility in the first place.

So having said that I would like to emphasise that the cost which often gets quoted with those mistakes is not a real cost, it's an unrealised opportunity cost and sure it hurts, but you know what, the same company culture that allows such mistakes to happen and miss out on opportunity costs is the same culture which also allows engineers to quickly roll out important features and updates and therefore create more opportunity in the first place, and much faster as a whole, so in theory the cost doesn't come without the opportunity and it all evens itself out. Don't feel too bad about it.