Their fifth trophy this year had appeared to have secured the Spaniard's job after a sticky domestic spell but his call for new signings or else he would speak with his agent about his future has not gone down well.
Asked if Benitez's comments had ruined the party after Saturday's 3-0 final win over TP Mazembe in Abu Dhabi, Moratti said: "No, for the moment no. Perhaps they were a little inappropriate given the situation. Right now Inter fans are happy.
"At the moment I am not talking about Benitez," he added on his return to Milan.
Former Liverpool coach Benitez only took over at the European champions in June after treble-winning Jose Mourinho left for Real Madrid. He asked for new players for the start of the campaign but no signings materialised and a subsequent injury crisis has contributed to champions Inter lying 13 points behind leaders AC Milan at Serie A's mid-season break.