The Essex side are rooted to the foot of the table, and following a 2-1 loss to Sheffield Wednesday on Tuesday night are now 10 points from safety.
"It will take an amazing run of results to get out of it but we'll keep going," insisted Williams.
"It's a proud man who walks out in a Colchester shirt and we've got to do that until the end of the season."
The Us have nine more games to play this season. Scunthorpe and Leicester City also make up the bottom three.