You need to be taking days off to recover if you are just starting running at this pace. It may just be overuse of the knee that is causing you soreness and since you said after rest it was better, taking the recovery days should be all you need.

Behind the knee: that would probably be the popliteus muscle.  I'm about 4 weeks into C25K, and I get that sometimes.   I think some sort of step exercise might be used to strengthen the popliteus.  I'll probably try to incroporate this into my strength training routine at some point.

Be very careful with pain behind the knee.  If the knee has problems that cause swelling it usually shows up as pain in the back of the knee.  I went to the doc/surgeon in 2007 with pain behind my knee (wasn't a runner then) and his first words to me were, 'soreness behind or in back of the knee is generally swelling because of a larger problem within the knee'.  Two weeks later I had my first of two knee surgieries to repair damaged ligaments (the second surgery was in 2010). 

I'm VERY careful with my knees.  I'm hoping your pain is from over use.

Cheers!!!

Glad to hear it Paula.

I'm still able to run, I limit my distances to 6 miles or less.  The second surgery was mostly my fault, I didn't 'listen to my body' when I started running. 

'Play through the pain' was the saying when I was a much younger athlete.  Now, not so much. 

Cheers!!!