Good post mate. I suppose what I meant by not taking it seriously is no manager in Everton's history has ever deemed the league cup as important enough to go ahead and win it. And in the fans eyes no manager has ever been judged negatively because of their inability to do so.
The league cup may have been won by "top teams" but it's won by top teams playing heavily weakened, often bordering on youth teams. Chelsea had players making their debuts last night.
I agree with you, we are in the same bracket as these teams and should treat this competition the same way they do. IE it is an opportunity to win a trophy, but also a chance to blood squad players and young players into the side.
Alternatively you get small teams like Boro, Birmingham and Blackburn who tale the trophy seriously, give it their all and in all honesty by doing so they have massively messed their clubs up in the process. Going hell for leather for a cup the top teams don't care about and trying to use it as a stick to beat an Everton manager with is the behaviour of small teams. The one exception to this is Kopites who carry on like the trophy means something. They also have a small club mentality. Their owners don't like, they sacked a manager even though he won the league cup. That tells you all you need to know about it's importance.
There has also been a lot of evidence to show that "big" clubs like Spurs have really struggled after they win the league cup in the league.
I should make it clear I am not against trying to win football games and trophies. What I am against is people inflating the importance of this competition and using it as a way to knock the manager. I also agree with how Martinez is using it, as a way of giving opportunities to fringe players and younger players. It's all part of developing a broader squad.