Applying to PhD programs as a Masters student with no Internship experience I am a Computer Science Masters student at University of Washington and I am planning to apply to PhD programs in the US.

I started my Masters in September of 2015 and am going to complete it this December.

Since I came from Electrical Engineering background, I had to spend a significant portion of the past year learning the ropes(various kinds of algorithms etc) and in the process also got very interested in research.

I also worked under a professor on a project that received a small NSF grant.

The problem is I don't have any paper publications or internships. I didn't have an internship as I found it hard to crack the coding interviews since I wasn't very skilled in programming back then. Since then I have improved significantly.

And I will also be participating in another research project starting September 1st.

Extending my Masters course is really not an option since the tuition is exorbitant. So I can't take another year and do research.

Will the PhD admissions committee hold it against me that I don't have any publications or internship experience? If so how do I make a good impression on them so that they consider me for admission?
In the UK an internship is not necessary.  In general, an internship is just one way to prove yourself, a paper is another, but good letters of reference can compensate for these.  Generally it's good to have a good mix of skills in your lab.  Don't be defensive about it; just talk about your assets.  

On the other hand, if you don't get the PhD offer you want, you might find a research position (or a job) and get some additional research experience that way.  There's always next year for applications.