The 37-year-old highlighted the importance of beating Serie A's in-form side, and played down the reported bust-up with Antonio Cassano
The Nerazzurri found themselves two goals down after less than 20 minutes on Sunday, but two goals from Rodrigo Palacio inspired a sensational turnaround.
"We started very badly, due in part to an amazing atmosphere here in Catania, and our opponents began very strongly," Stramaccioni was quoted as saying on the club's official website. "We made a huge mistake on their first goal and on the free-kick with [Giovanni] Marchese getting up on his own. But if the team didn't have guts, there would have been no way of coming back.
"It was a huge win because we beat the form side in the league at the moment. It's even sweeter because I don't know if anyone would have backed us after the first half. In the end we deserved the win."
Palacio came off the bench to fire his side to their dramatic victory, but Stramaccioni defended his decision not to field the Argentine attacker from the start.
"A coach is not a journalist, so I'll remind you that [Palacio's] performance was good enough based on the service we provided him," he said. "I left Palacio on the bench because we have lots of matches coming up and I have to manage that."
Antonio Cassano was dropped from the side following a reported training-ground bust-up with Stramaccioni, but the Inter coach dismissed the confrontation as part and parcel of a competitive dressing room.
"There's training tomorrow and Antonio will be there just like the rest of his team-mates," he added. "And we'll prepare for Thursday's game. When will he be brought back in? There's no need to bring him back because he was never excluded in the first place. There can be heated discussions in any changing room.
"We'll need everyone between now and the end of the season, and that includes Antonio Cassano. But what goes on in the dressing room is our business alone. These are all things that happen between men in a dressing room."