Inter probe Mourinho row with reporter
Reports have said a heated argument took place outside the team bus but Mourinho, who was banned from the dugout for the match, has not commented.
"For the moment I don't want to comment as I still don't have all the facts, but I'm sorry," Moratti told reporters.
Italy's sports journalists' union, already upset by Mourinho's confrontational attitude towards reporters in recent weeks, has urged Moratti to act against his coach.
"I will talk to the head of the union to find out what he means by 'strong action'," Moratti added.
Mourinho, who won the Serie A title in his first season in charge last term, has lamented the constant grilling he receives from Italian media and has sometimes boycotted news conferences.
Some reports have speculated he may leave the Serie A leaders at the end of the season because he feels so harangued.
The outspoken Portuguese, who won two Premier League titles with Chelsea, previously said he will see out his contract until 2012.