Keane, who was covering the match for Sky, brought up Ireland’s 5-1 World Cup play-off loss to Denmark in 2018.
The United legend was Martin O’Neill’s assistant manager at the time, and it looked like the Boys in Green were headed for the World Cup when Shane Duffy scored early on at the Aviva Stadium.
However, Denmark replied emphatically and Eriksen helped himself to a hat-trick.
Addressing the Dane, who was one of the key men in United’s 3-1 win, Keane said: “I have no questions to ask you because I’m still upset over Dublin, when you scored for Denmark, so I’ll pass you on. I’m still upset with you.”
Eriksen saw the funny side as he replied: “It’s a good night out in Dublin.”
The victory over Arsenal made it four in a row for Erik ten Hag’s side, who have bounced back well from two defeats at the start of the season.
Keane was critical of Arsenal boss Mikel Arteta after their unbeaten run was ended by United.
“I’m fed up of all their excuses. I’m serious.
“Arteta gets interviewed after the game, he’s a sore loser, like us all.
“He’s got to give a little bit of credit to Man United but he never does. Every time he loses a game it’s all about what the opposition didn’t do properly or the officials. Stop making excuses.
“You lost the game 3-1, you’ve done okay. Take your plaudits but give me the points any day of the week.”
Keane remains a popular figure at United, and the spectators who stayed behind to celebrate the win launched into chants in his honour.