Arsenal have appealed for help in identifying the person responsible and will ban them for life when they have done so.
The Football Association will, meanwhile, consider whether to launch their own investigation into the unseemly events at the stormy game, which the home side won 1-0.
Carragher was punished by referee Mike Riley, who dismissed him for violent conduct after he picked the coin off the ground and hurled it back into the crowd.
The defender later issued a statement on Liverpool's official website, admitting: "I regret what happened at Highbury today because I let the club, the fans, my team-mates and myself down.
"No matter what the physical or verbal provocation, I shouldn't have reacted like that and I want to apologise for any offence I've caused.
"I was frustrated and I did it without thinking in the heat of the moment.
"Everyone who has seen me play regularly will realise that it was completely out of character, but I'm not trying to make excuses.
"It was wrong and, as a professional footballer, I should have known better. It's a mistake that I won't make again."