A lot do realize it, which is why it's annoying to hear it. Asian describes half the world's population. That doesn't narrow it down very well.
At least one eyewitness described the suspect as Asian, which is probably why the press said it that way. The danger I see is that a lot of people have it in their heads that terrorists have to look like Arabs, or middle easterners. That kind of tunnel vision is dangerous.
Why should it be annoying at all? England has many colorful "limey-isms" that are endearing. It's like our news reporters calling illegal Mexicans "cement workers"; it's a commonly shared code word.
As long as you know where Asia is and what's in it, what does it matter?
I have my Limey irritation too, but I just suck it up: "it is feared that..." as an affectation, where fear is not part of the story.