As a non-researcher, how to tell new knowledge that the speaker might not know? A talk was closely relevant to a problem which had no breakthrough for a long time, but the speaker didn't seem to know a recently new method which is proved be able to solve it yet. What should I do? 

I was not a researcher, relative young comparing to the large amount of attendees, and this was the first time I attend an international conference all by myself. Whether the audience interacted with me or not, they could always notice me as I was the smallest person sitting in the front row (for note taking, the rest of rows didn't have table) in between old, big/tall Western professors. Not to mention my broken English.

I had asked the speaker if he knew any new method to solve the problem or not, and he said no. I think he and the audience did have an interest to hear it (I could even mention some leading names working on it), and I know that most of them didn't really care what I mention above at all, but still with that much pressure I didn't have enough confidence to say. Since the new method comes from a completely different field, it might take a couple minutes to explain it. The longer I talked the more embarrassed and tongue-tied I was. In the end I thanked him and asked no more question.

I know that everyone has their first time, but what is your advice in this exact situation? What would you do to feel relief yourself? The impact of the newfound knowledge is big, and yet I'm a non-researcher. That pressure is not an easy thing for an inexperienced person to handle.
It's perfectly fine to use the question period to alert the speaker to other related work.  As with any question, try to keep it brief: one or two sentences.  I agree that a &quot;couple minutes&quot; is too long.  Here are some sample phrasings.

There is a recent paper by Jones and Smith on reticulated splines, in which they propose a method to solve the trolley problem.  Would this help to resolve the issue you mentioned in your talk?
Are you aware of the recent paper by Jones and Smith which gives a solution to the trolley problem?  This seems like it might helpful in answering your question of whether splines can be reticulated.
You mentioned that you need a solution to the trolley problem.  There is a recent paper by Jones and Smith which solves this problem using the method of reticulated splines.  Does that seem likely to be workable in this case?

It is a good idea to mention the names of the authors - partly to give them credit, and partly so that the speaker or other audience members can look up the work later.
Try to resist the urge to explain the related work in detail; the question period is not the time for that.  If there are significant aspects of the paper that are very relevant (special techniques, limitations, etc), you can mention them briefly (again, one or two sentences).  Otherwise, you can certainly approach the speaker after the talk is over, during a coffee break, etc, for further discussion.