The 31-year-old appeared at Staines Magistrates' Court on Monday to admit a public order offence from December 17 near Mishiko bar in Reigate.
Puncheon told the bouncer who confiscated his belt to 'keep it and buy a house with it'.
A further charge of assault by beating was dropped as no evidence was offered by the prosecution.
Craig Warsama, prosecuting, said: "Mr Puncheon stated he was provoked during the course of the evening at the nightclub. At 2.15am on the 17 December police were called after Mr Puncheon utilised a belt during the course of a disorderly melee.
"Mr Puncheon is seen to take off his belt and began lashing out at members of the public. 'He was described as irate and is shouting 'arrest me', 'arrest me'.
"He began to tell officers that if he was not going to be arrested he is going to run away with his friend and he is seen to begin running away for a few seconds before an officer pulls him by the arm and detains him.
"Puncheon can be heard to utter threats to an unidentified person and the comments were unnecessary. 'Mr Puncheon is offered his belt back by Mr Mendy but Mr Puncheon replies 'keep it, keep it, buy a house, keep it keep it'."
Palace boss Roy Hodgson has vowed to punish Puncheon, who has been out of action since New Year's Eve with a knee injury, only if he is found guilty.