The Rotherham winger came on as a second-half substitute in the 0-0 draw with Hungary in Budapest.
In doing so, he became the first player of African descent to represent Ireland, having been born in Nigeria but moving to Cork as a youngster.
Ogbene, who missed most of last season for the Millers with a serious knee injury, did not get much more than five minutes, but he relished every second.
“I am over the moon. It is a very proud moment for myself, my family,” he said.
“I have always dreamed about making my international debut so I am so blessed that I did it with Ireland.
“These opportunities don’t come very often and after the season I had to get this opportunity is a great honour.
“It is a great achievement, I didn’t even know that was a thing because I have seen players from different backgrounds play for the Republic of Ireland
“It is something I am going to carry and cherish for the rest of my life. I want to inspire young kids and hope they take courage and hope he they can take the leap.”