Jesus has developed into a lynchpin in Stramaccioni's defence since making his first start of the season at Torino, who visit the San Siro tomorrow night.
Such is his new-found confidence, the Brazilian believes fourth-placed Inter are capable of chasing down Serie A leaders Juventus, booking their place in the Coppa Italia final and succeeding in Europe without too much difficulty.
He told inter.it: "I want to win everything - the Coppa Italia, Europa League and give everything in the league. Can we do it? Yes, always.
"I'm eternally grateful to Stramaccioni for the faith he's shown in me because, as a player, it helps enormously when you know you've got the coach's backing."
Stramaccioni made wholesale changes to his starting XI after witnessing a 3-1 home defeat to Roma in September, with an unproven Jesus playing a key role in a 2-0 win at Torino in the following game.
"I remember it well because that match changed my situation," Jesus added. "I've started playing every game since then but, as I've said, I still need to improve a lot to be able to win trophies."
Inter are looking for a new playmaker. The treble-winning Wesley Sneijder has now departed for Galatasaray, with Philippe Coutinho reportedly attracting an approach from Liverpool, and the Nerazzurri have now been linked with a move for Corinthians midfielder Paulinho.
Speaking about the latter, Jesus added: "I know him, he's a great player. He always gets into the box and scores a lot of goals. It'd be great for us if he does join Inter.
"What about Coutinho possibly leaving the club? I'd be sad but he needs to do what's right for him. However it goes, whether he leaves or not, it won't change our friendship."
There is renewed optimism at Torino, who are up to 11th place in the table on the back of three wins from five games.
Goals from Mario Santana and Alessio Cerci handed Il Toro a 2-0 victory at Pescara and club president Urbano Cairo was delighted.
He said: "I went to see the coach and all the lads to compliment them for the great win at Pescara, but also to ask them to stay tighter and concentrate harder.
"We have to continue with the same application on the field and, if the performance is there, the rest will follow."