A court heard Aidan Chaves, 26, reacted angrily to taunts from fans and was spat on during a home game for Sawbridgeworth Town FC on 25 March.
But he denied screaming threats at Clacton supporters on the touchline at the Hertfordshire club.
Stevenage Magistrates Court adjourned the case for a later hearing to decide if he had made threatening comments.
The three magistrates were told that Chaves faced derogatory remarks from the fans of the opposing team, including songs about his skill as a player, his tattoos and his mother.
One fan is said to have spat on him as he prepared for a throw in.
The court heard Chaves ran from to the changing room and emerged carrying a broken corkscrew.
Prosecutor Prosecutor Rufia Khatun said that, holding it aloft and running towards the Clapton fans, he allegedly screamed "Come here. I'm going to cut your throat."
Chaves - who gave his address as Mount Mellick Road, Portlaoise in the Irish Republic - pleaded guilty to a charge of having an offensive weapon in a public place.
The court was told he entered the plea on the basis that he had not uttered the threats that had been referred to by the prosecution.
In a statement he said he had grabbed the corkscrew to "ward the fans off".
Magistrates adjourned the case so that another hearing can take place on 10 August to decide if he had made the threats as claimed by the prosecution.
Chaves was granted unconditional bail.
A footballer accused of threatening fans with a corkscrew has admitted possession of an offensive weapon.