Your team has a dynasty. They have accomplished a great deal, winning so many games for several years. 3 out of 4 Superbowls. You have the trophies, rings, commercials. Heck, you even drafted the Diet Pepsi machine, got Willie doing some god awful dancing, and Tom Brady is doing Visa commercials with the Metaphors.
Do you think that the attitude that your team does not get the respect it deserves is that you can't have an underdog mindset unless you can find a reason?
As far as the media. You will always find articles in the media playing up most any team, why? They sell! Find an article counting the Patriots out, it will sell to Pats fans because they love to read the bad stuff to stoke their emotions, good "BB" material. Find and article touting the Pats, it will sell because it can be used to see that the media is "finally getting it". Same way with every other successful team. Sorry the Colts get a lot of media attention too, it must make somebody some money.
It will be a rare day when droves of other teams fans come and "kiss the ring", first whats in it for them? and second because it is just too much fun for them to watch you all spin up when they won't declare your team a "dynasty".