Well, I think you have to think about whether this is an anti-American alliance, if indeed an alliance exists and is not merely sensationalism by the media, or a pro-themselves alliance. Here's the way I see it. Venezeula, Syria and Iran (not NK, they're ****ing crazy) can't be said to be anti-American, because they're not out to "get" America. They're not the ones who attacked New York, they're not assassinating leaders and financing seperatists or waging economic warfare or anything like that. These nations only oppose US influence in their region, which is a completely legitimate stance. As far as I'm concerned, the US shouldn''t have any influence in the Middle-East or Latin America to begin with, and efforts to dictate to these places how things should go are bull****. If America pursued a non-interventionist foreign policy, as all nations should, it's very likely that the grievances these guys have would disappear and they wouldn't be able to rally popular support.
I have particular beef when poeople say that for example Iran is anti-American. Projecting US power, or any country's power, across the world is not a right, and when someone calls you on it he's not attacking America, he's attacking the idea of America is a the world's judge, jury and executioner.