A surprise 3-1 defeat to struggling Siena saw the Nerazzurri slip out of the Champions League places and into fifth, with Stramaccioni registering just one win from his last seven games and collecting only five points.
Daunting fixtures against Chievo and Fiorentina precede the second Milan derby of the season and the Inter boss now finds himself under pressure to keep pace with fourth-placed AC Milan, who have been boosted by the arrival of former Inter striker Mario Balotelli.
But when asked if he still had confidence in Stramaccioni, Moratti told inter.it: "Yes, of course, of course.
"We need to work hard and we need to pay more attention. We need to protect ourselves from our rivals, especially those nearest to us.
"But we do need to turn things around."
Reports in Italy suggested Moratti had sent his coach a text message detailing the bare minimum that was required over the next five games.
"No, I never sent a text message," he added. "I read that too but I never sent a message. I did have a little chat with Stramaccioni though."
Rome-born Stramaccioni, who guided the Inter youth team to victory in the NextGen series, assumed interim control of the first team when Claudio Ranieri was sacked last March.
The 37-year-old was confirmed as permanent head coach after leading the Nerazzurri to victory in the Milan derby and reversing a poor start to the season to claim a sixth-placed finish.