Stramaccioni stepped up to take charge of Inter in March 2012, having previously managed the club's reserves, replacing the sacked Claudio Ranieri.
Inter are currently fifth in Serie A, but a 4-1 defeat to Fiorentina led to more speculation over Stramaccioni's future.
Recent reports in Italy suggested that the 37-year-old had five games to turn Inter's fortunes around, but Moratti has backed the former Bologna defender, whose playing career was cut short by injury.
"Stramaccioni has never been up for discussion," Moratti declared. "He's always made a lot of sacrifices for the team and he keeps on improving."
Inter trail their Milanese rivals by two points, and a win in the San Siro could see the Nerazzurri move into third place in the Serie A table.
"We hope the pressure will get to Milan this weekend," Moratti added. "I'll just ask my players to give their all.
"They have to respect the shirt and continue chasing third place in Serie A which is our objective."