The Nerazzurri has endured a difficult campaign that now sees it restricted to an eighth-placed finish at best - an outcome that demands victory over Udinese with Catania required to drop points against Torino.
Whatever happens, Inter will not play European football at San Siro in the northern autumn for the first time since the 1999-2000 season.
Moratti has consistently backed his 37-year-old coach, who led Inter's youth team to the NextGen title last year, citing his unwavering resolve to succeed despite a debilitating injury crisis as the saving grace in his first full season as a Serie A coach.
The oil tycoon was unwilling to give any further guarantees on Monday, however.
He told inter.it: "There's one more match left to play, let's just let them get on with it in peace.
"You're fuelling doubts, not me. You're the one asking me if I have any doubts, and I don't have any at the moment."
Moratti also rejected speculation he is ready to sell a 51 per cent share in the club to a potential foreign investor by the end of May.
"I read that too, I think somebody just made it up," he added. "I don't think so. I haven't looked at everything properly yet."