Gallagher required several stitches but returned to continue the celebrations and even later saw City manager Pep Guardiola.
Speaking to TalkSport Breakfast with Laura Woods, Ally McCoist and Jamie O'Hara, Gallagher added: "I don't see the last two minutes - I've got to get taken down by the St John Ambulance and had to get stitched up. I've got stitches in my top lip, I've got two black eyes. As I'm going down the corridor Pep's running up crying and we kind of hug each other and he says 'what's up with your face?'
"If you've seen me today [Monday], I look like I've just arrived home from the eighties, from Elland Road. I look like I've had my head smashed in. It's unbelievable. A lot of City fans are asking, 'You alright? What's happened?' and I said - you'll never guess."
The father of the Portgual international Dias was unhurt in the incident. "Not a mark on him," said Gallagher. "He's a big bear of a man - he almost knocked my teeth out. But as days go at The Etihad that's got to be up there with the best."