Stramaccioni, 37, was initially chosen as an interim coach last season and was seen as the bright, young revelation of Italian coaching until a couple of months ago.
Now he finds himself in danger of becoming Serie A's 11th coaching victim of the season after a run of one win in seven league games culminating in Sunday's abysmal performance in a 3-1 defeat by second from bottom Siena.
"Things can go well until a point but then something might go wrong, be it injuries, form or refereeing decisions," said Moratti who has fired four coaches in the last two and a half seasons.
"I'm not saying it out of stubbornness, I think Stramaccioni is a bright coach," he told the club's website. "He works to make things run smoothly and he suffers when things don't go well.
"Things aren't going terribly but nor are they going well. The players need to know the fans believe in them," added Moratti.
"The crowd must stay with them, make themselves heard. The players care, what's important is making the fans happy."
Malesani's predecessor Gian Piero Gasperini was fired following Sunday's 2-1 home defeat by Atalanta even though he was not on the bench, having been suspended following a row with officials in a previous match.
"I hope to see the new Argentine players settle in as on Sunday they were thrown straight into the starting line-up for the most important game of the season and some of them hadn't played for months," said Zamparini.
"For that I will never forgive Gasperini."
He inherits a side that boast Serie A's best goals tally this season (49) and second worst for goals conceded (42), a reflection of their former coach's attacking philosophy.
