Last season's beaten finalists visit the Stadio San Paolo for their Group F opener, and Watzke has identified the Italians as serious challengers for the top spots in the group following a summer spending spree which saw the likes of Jose Callejon, Gonzalo Higuain and Pepe Reina join the club.
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"The Champions League is not like a normal season; it's more like a cup competition. You must be ready from the start."
Watzke went on to stress that the team have not been affected by the increased publicity and attention following their remarkable run to the final in 2012-13, where they were beaten by domestic rivals Bayern Munich.
"A lot of things have changed," he said. "If you reach the final of the world's biggest club competition, you receive a different level of attention. But that doesn't affect us; we are the same as before."
Wednesday's clash at the San Paolo kicks off at 19:45BST.