The 25-year-old passed away on Saturday afternoon after suffering a cardiac arrest during Livorno's Serie B match at Pescara.
Moratti's Inter side were due to face Morosini's parent club Udinese in Serie A action but he believes that the game was correctly postponed.
"We have to do what is right. I don't think it is the case to create any controversy at this time," Moratti told the club's official website.
"I think it was obvious not to play the game. It was the only choice that could be taken because it was a serious episode, which sent the right message.
"For Udinese players, it was a case of losing a team-mate, a team player, who everybody knew well. Hence, it was a very serious situation, a horrible episode and the football world understood it."
The fixtures scheduled for this past weekend have been rearranged for April 24 and 25.