The supporter in question has since been arrested and has been issued a lifetime ban.
The Newport striker secured all three points for the Welsh side, scoring two first-half penalties at Priestfield in their 2-0 win.
However, the game took a vile turn when a supporter charged to the front of Gillingham's Rainham End and made a racist gesture towards Bogle during his goal celebration.
In a statement posted on his Instagram story following the incident, Bogle said: "Firstly I want to thank everyone for the messages of support already after today's match.
"Listen this problem is bigger than just football but in life and as we keep saying, there's no place for racism. It's 2023. Do better.
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"I appreciate the support I received from the Gillingham players and staff and also a lot of the supporters and I urge you all to continue to drive out the minority that stain the clubs reputation and values.
"I also think it's weird and a bit alarming that Sky Sports have decided to cut short the footage after I scored both goals.
"Don't hide the fu*kry, let it be seen in plain sight so everyone can witness the behaviour that is still very much alive in all walks of life and in our game at all levels. #CantStopWontStop."
During the game, the club's director of operations, Joe Comper, took to X following the incident, writing: "Disgusting from one individual in the Rainham End. Arrested, and a lifetime ban from Priestfield issued.
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"Can't thank the large number of fans from around the stadium who are clearly as enraged as us. We really appreciate your support."
The club then released an official statement after the game, stating they have 'zero tolerance' for the behaviour and confirming the supporter in question had been given a lifetime ban.
Kent Police have also confirmed the individual had been arrested.
Gillingham owner Brad Galinson took to X on Sunday to condemn the behaviour, stating three others were also ejected from the ground during the fixture for 'sexist/homophobic chants'.
He wrote: "Nearly all Gills fans are good people just there to enjoy the day. One was not & will never be welcome at Priestfield again. 3 others ejected for sexist/homophobic chants. They will either learn how to behave or not return. We will not stand for it! Help us help you."
The FA recently issued the club a £12,500 fine and ordered it to form an action plan to eradicate abuse inside the stadium following three incidents last season involving racist and sexist comments.