The 43-year-old referee, who was previously fired after a video revealed controversial comments he made about former Liverpool manager Jurgen Klopp, only spoke to confirm his name and entered his plea during the hearing in front of Judge Shant KC.
Coote was charged in August with creating an indecent image of a child, and he initially pleaded not guilty to the charge at a hearing in September at Nottingham Magistrates' Court.
The judge ordered a pre-sentence report to be completed before sentencing, which will take place on December 11th. Coote was instructed to appear in court again on that date after pleading guilty.