The 30-year-old beat off a strong challenge from striker Leigh Griffiths to pick up the award at the Supporters' Association annual dinner last Sunday.
Williams started out as a Manchester United trainee in 2002 before moving on to Crewe, Carlisle and Colchester, but he believes he has still to reach his peak.
He said: "I would say I am getting to the place I want to be as a goalkeeper. I would say that I am arriving into my peak, both fitness-wise and in terms of experience and mentality.
"In the last five seasons I have had three player-of-the-year awards. I got player of the year at Carlisle and in my first year at Colchester.
"So it is good recognition for me and testament to the amount of work I put in to try to get to a consistent level of goalkeeping.
"With goalkeeping, it is such a long learning curve, early on in your career you just don't perform consistently.
"You will have games where you are amazing and you will have games where you will make mistakes and you will probably dwell on the mistakes too long and are overly critical of yourself.
"But the next few years will be my peak time and if I can pick up more awards that would be fantastic.
"You are always judged by your mistakes and if you don't make many mistakes then people will have you down as a reliable goalkeeper so long may that continue."