The Nerazzurri dropped to seventh in the Serie A table following Sunday's 2-0 defeat at Cagliari - the Milan club's fourth loss in five league outings - with the last Champions League place now nine points away with six games remaining.
Two more key players joined a lengthy injury list on Monday, with midfielder Walter Gargano and defender Yuto Nagatomo both suffering leg injuries to leave Inter with a selection dilemma ahead of Wednesday night's Coppa Italia semi-final meeting with Roma.
But it is the serious personnel crisis - which has seen senior strikers Rodrigo Palacio and Diego Milito ruled out of several important fixtures - that convinces Moratti his 36-year-old coach has been working at a clear disadvantage for most of the season.
He told the Gazzetta dello Sport: "I can't do anything else but support Stramaccioni, based on all the difficulties we've had to deal with this season.
"We are going through a difficult and quite dramatic season. In terms of the injuries, I hope we can come up with a solution, but it will be difficult.
"But a little bit of invention and good luck could see us through."
Moratti has also invoked the anger of the Italian Football Federation (FIGC) by suggesting match officials have regularly acted "without good faith" towards Inter, with other figures at the club publicly suggesting referees have favoured city rivals' AC Milan in their bid for a top-three finish.
The FIGC have summoned Moratti and his legal representatives to a disciplinary commission to examine his comments.
Meanwhile, Inter veteran Javier Zanetti says the priority now is to overcome Roma and reach the final of the Coppa Italia.
Zanetti told the club's official website: "We want to play well against Roma on Wednesday. There's no point talking about the match against Cagliari as we can't do anything about it. Now, we need to think about performing well on Wednesday.
"We'll try to prepare in the best possibly way for the match versus Roma and we hope to get a result that will see us into the final.
"At the end of the campaign, we'll look back and review everyone's performance. Then we'll begin to prepare for next season as we always do."