It was incorrectly reported that league rules required a player to be on the roster for at least 41 games -- or at least one game in the Stanley Cup finals -- to have his name on the Cup. Bickell was under the same impression.
But a league spokesman said a few years ago a resolution was passed that the winning team can choose 52 names to put on the Cup.
Bickell played in 16 regular-season games and four postseason games.
"It doesn't really matter to me," Bickell said. "It kind of hurts that it's not on there ... but I was up and down all year."
Twenty-three players and 29 front-office personnel had their names on the Cup.
"[The Cup] just shows the core, and it doesn't start with the players, it starts with the people upstairs, too," Bickell said. "They help a lot and make everything happen. So I understand. Maybe next time."
A Blackhawks spokesman said the team would have no comment on the process of picking names.
Bickell received a Stanley Cup championship ring with his teammates on Wednesday.