The holders, who had already qualified for the last 16 albeit unconvincingly, were embarrassed 3-0 by eliminated Werder and now head to the Club World Cup in the UAE desperate for success to help the Spaniard cling to his job.
"I don't want to create problems before or during the World Club Cup. Afterwards we'll see," Moratti told reporters on Wednesday.
"Benitez must have character because if not, we won't win the World Club Cup."
Inter, who have lost seven games already in all competitions this term, face a semi-final on December 15 before a potential final with Brazil's Internacional on December 18.
Last season's top scorer Diego Milito could return for the Club World Cup after over a month out injured but even the Argentine looked off form earlier in the campaign and the purchase of a striker in January looks certain.
The sunshine of Abu Dhabi at the World Club Cup may be a welcome break from Milan's wintry temperatures, but for Benitez the heat is very much on.
