I think the difference between the Woy era and now is that even when Woy was hired people expected nothing but mediocrity and everyone was combined in expecting terrible football and results as well as wanting him gone. Instead of that collective now, we have a disjointed support. Some people supporting Dalglish because of his past, some people supporting Dalglish because their parents/older relatives/older friends have drummed it in to them about what Dalglish is, who he is and why he should be respected. Then you have some people objectively criticising Dalglish as well as the normal over the top idiots.
This has basically resulted in a lot of infighting which has eroded any sort of optimism or collective feeling.
Also, with the first few months of Dalglish's tenure holding such promise it is worse to see what the team has become now, whereas if Dalglish had presided over a team as bad as the one under Dalglish people would not have had any optimism for this season anyway, so a League Cup win would be seen as amazing regardless of the league position.