Black had scored a late winner in extra-time and was about to head into the tunnel when he was struck.
The Coleraine player was left with a swollen lip and bloodied nose as a result of the incident.
“I was just walking down the tunnel and saw somebody coming out the corner of my eye,” Black told BBC Northern Ireland.
Black added that there was “no place in football for that kind of stuff”.
There were also skirmishes between a small number of home supporters and stewards before calm was restored.
A Cliftonville statement said the club condemned those involved in the scenes.
“Cliftonville Football Club, with the help of the Irish Football Association and other authorities, will in the coming days look closely at the events that occurred and will take appropriate action in addressing any issues arising from our investigations,” added the statement. “Cliftonville Football Club wishes to condemn any persons involved in actions that tarnish our club. Numerous people work tirelessly for the good of our club as volunteers, both on match days and throughout the season, and such incidents are not a just reward for their efforts nor for supporters or indeed players.”
Coleraine manager Oran Kearney also condemned the assault on Black but praised the Cliftonville stewards and said no blame could be apportioned to the North Belfast club.
“I was about 20 yards behind and I didn’t see it but you can’t legislate for things like that,” said the Coleraine boss.
“It is by no means the fault of Cliftonville. That could have happened at our ground. It’s as simple as that. When emotions run high at the end of games, you can’t legislate for every single person who walks into your ground. I thought the stewards did a good job trying to get people off the pitch. I’m sure the powers that be will look at that and hopefully punish the perpetrator.”