The 24-year-old Serie A top goalscorer from last season was unable to find the back of the net at the World Cup, but Watzke says that is no reason for anybody to doubt the qualities of a man they paid almost €20million for this summer.
"Ciro didn't have one game at the World Cup in which he could really prove himself," Watzke told Sport Bild magazine.
"The Italians should be happy that they've got such a great player for the years to come rather than making him responsible for everything.
"It would be like blaming Erik Durm or Matthias Ginter if things go wrong for Germany."
Watzke does not expect the World Cup disappointment to have any lasting effects on Immobile when he links up with his new team-mates, however.
"As soon as he arrives here, he's not going to think about the World Cup even for a second," he said.
"We're all looking forward to him arriving."