Sorry to say that I think you're on rocky ground on this one mate. It sounds unfair that the police decided to adopt a commonsense approach and not to take it further yet you've still been banned by the club. Trouble is, the club have a right to ban who they want even if you've not been convicted of anything - maybe not the best analogy but I'd compare it to being barred from a pub.
A similar thing, albeit a different offence, happened to my mate on the day we won the title against West Ham - when Kompany scored the second goal somebody (not my mate) set a flare off in our section. It ended up on the floor near us and my mate somewhat naively picked it up and waved it around his head for no more than a couple of seconds before dropping it. About 10 minutes later the stewards turned up and he was arrested. The police let him go without charge about an hour or so after the match ended and he met us in town to join in with the title celebrations. We all thought that was that but a few days later he got a letter off the club saying he was banned for the whole of the following season. We all thought this was OTT as the police themselves had been decent enough about it. He sent a letter of appeal to the club, explaining that he wasn't the one that had set it off, it was a moment of madness in the heat of a goal celebration, etc, but while they acknowledged that it wasn't him that set it off, they still upheld the decision to ban him - I think the fact that he was "in possession" of it at some point meant that it was still an offence.
If you only end up with a 3 game ban, it's probably advisable to take it on the chin. If it turns out to be full season, there's no harm in appealing it but looking at what happened to my mate I can make an educated guess at what the outcome will be.