You are wise to ask questions about this situation.  Often children who are age-right for Kindergarden are not quite ready for the increasingly academic demands of today's school programs.  Maybe he just needs a bit more time. Boys especially can benefit from being a bit older in their class. Can you find a developmental, play-based Kindergarden as a transition for him?

Perhaps there are other issues going on.  He might be very sensitive, to sounds, or to large groups.  Your first stop should be your pediatrician.  Ask him or her about sensory processing, and if your son might benefit from a deeper look.  

The best advice of all is to not worry, or feel that you need to rush.  Your concerns will telegraph to him, and he may get more anxious.  Take your time, and let him take his.  

Below I've linked an article on School Readiness by developmental pediatrician Dr. Susan Johnson.  Best wishes.

As a kindergarten teacher, I don't think that "scared and shy" is reason enough to retain a child in preschool. Does he like school? Enjoy stories and songs? Enjoy interacting with other kids his age? Is he showing an interest in reading and writing? Can he write his own name and identify the letters in it? Can he follow simple 2-step instructions?  These are the things I look for when asked to assess a child's readiness to be in my classroom.  Is it possible for you to request a kindergarten teacher with a gentle demeanor and sets a quiet tone for the classroom?  Also: is your preschool in the same school as the kindergarten your son will attend? If so, can you ask a kindergarten teacher to spend some time observing him and give their opinion?  There is little advantage to retaining kids who are of the appropriate age, so I would definitely seek feedback from another teacher or school admin who can see your child in action.

My son had the same issues at that age. I found out later, by being proactive, that he had a processing dyslexia. And, that he needed glasses. He was also very outgoing at home because he was familiar with the environment.  It could be that he has difficulty dealing with chaos in the classroom.
Suggest getting the school counselor activated, but don't rely on them to do their job. Have a objective IQ test and assessment performed  by your personal doctor/ psychologist. Sit in the classroom and observe the teacher for your self, you have the right to do so. (Videotape the classroom if you can receive authorization by the school board.) And, any communication between yourself and the teacher should be documented with copies going to the school, school board, the district school supervisor, and the state board of education. The teacher, counselor, and/or principal are under no obligation to report any issues further up the educational rungs. Nor will they to protect their own interests.  Also, if you child requires any additional aids, the state has access to additional funding to educate their instructors.
Word to the wise, you have every right to review any and all information in your child's' records. The school has two sets of records by the way. These records are releasable immediately upon request. You do not need an attorney to see all of your child's' records. You have the right to remove any and all information in the file that discredits you and/ or your child in any way.