The sinking of the Hood was certainly a major shock to the British public and even the naval staff.

One has to remember that HMS Hood had been by far the most powerful ship of the British navy for decades and thus became to represent the might of the British fleet. Thus she was colloquially known as "The Mighty Hood". She was used on foreign cruises to show the might of the Empire around the globe and becamle a sort of symbol for the British empire.

Taken into account the larger picture, although the loss of HMS Hood was a (moral) blow to the British navy, Bismarck was doomed in her mission. The British had such an overwhelming superiority in all sorts of naval assets that no matter what, she could be hunted down, and even worn down by inferior ships. (Compare with what happened to Graf Spee)

In the end her mission had to be aborted by a hit in the fuel tanks by the uncompleted new battleship Prince of Wales after Hood sank, she was attacked and fatally disabled by elderly torpedo bombers. She had to fight off attacks by a single destroyer squadron all night exhausting the crew.

In short she was gradually worn down, not by battleships , but by other assets the Royal Navy had in abundance.

By the time she came under battleship fire again, she was already in no state to fight, an almost immobile unmaneuvrable ship with an exhausted crew just waiting to be finished off (and knowing that).

Her "last stand" was futile and just cost many German lives, and was frankly target practice for the British navy.

The only way she could have influenced the war was like her sister ship Tirpitz did, staying in hiding, far away from the most immediate dangers and thus forcing the Allies to allocate a large amount of forces and resources to keep on the ready just in case for the unlikely probability she might come out of hiding to attack something.

I suppose you need to examine the question in regards a) those in the service involved b) Policy makers and strategists c) wider public. As for A). There were several enquiries into the loss of Hood. While Hood had been significantly redesigned post Jutland and certainly was not a thinly armoured battlecruiser such as those lost at Jutland, she was not as well armoured as modern battleship peers. Particularly in deck armour against plunging shells. The Director of Naval Construction Stanley Goodall felt that Hoods armour was a weakness and had planned increases during her scheduled but cancelled 38' rebuild. He also had made (slightly argumentative/contrary) suggestions that she be reduced to low risk roles or removed for a rebuild. These weaknesses were well known and either deemed acceptable or minor operational mitigation put in place. But despite all of the risks she was one of the few ships able to maintain 30 knots and better able to intercept German capital ships For example Admiral Tovey considered issuing directions to Admiral Holland in order to minimise the risk to Hood. Likewise in his approach and maneuvering towards Bismark Holland clearly favoured closing quickly head on in order to minimise risk to Hood. Holland getting himself out of a favourable position in part stems from his attempts to mitigate the risk to Hood. So to those involved the weaknesses of Hood were known and accepted. The loss in such a dramatic style with such a high loss of life was still was shocking.