Sunday night's 1-0 home defeat to Bologna ended a disappointing week for Inter after their Thursday's 3-0 Europa League loss at Tottenham.
A haul of eight points from eight games has seen the Nerazzurri slip out of the Champions League picture and into fifth place, with Stramaccioni pledging to make the most of the remaining 10 games.
Moratti was cryptic on Monday as he issue a veiled warning to both Stramaccioni and director of sport Marco Branca.
He told Gazzetta.it: "Branca says Inter will carry on as they are, does he? Under Stramaccioni and himself? I agree, but that's up to me to decide.
"If everything stays as it is, but with different results, then we will go forward together."
Inter were lucky to reach the break level last night, with Bologna allowed free rein at the San Siro before Alberto Gilardino's half-volley settled the match midway through the second half.
"It was a sort of collapse against Bologna yesterday [Sunday]," Moratti added. "It's hugely disappointing but we need to stay calm when evaluating the situation.
"We need to recharge our batteries both emotionally and physically. I don't know why the first halves of games have been so bad, I don't think the players are doing it on purpose.
"Maybe they are going out there scared. But watching us throw game after game away is getting quite serious."
Stramaccioni, meanwhile, does not fear facing the sack ahead of Spurs' arrival in Milan for Thursday's second-leg encounter.
"I make mistakes just as everyone does, I think," he told inter.it. "Moratti's vote of confidence? I just want to thank the president with results on the pitch."