The English club have lifted the trophy twice during their history, with back-to-back triumphs coming in 2001 and 2002.
The Tigers get their campaign underway on Friday when they travel to Ulster in Pool 5.
"It's going to be a difficult one," Cole told Sky Sports News. "Starting the European Cup on a Friday at Ulster, it won't be easy, but if you want to get out of the group you've got to win in places like this.
"It's a statement you want to make and Europe is what you get judged by. If we want to be in Europe's elite and stuff like that then we have to perform."
Leicester were knocked out in the quarter-finals of last year's tournament by eventual winners Toulon.