The Nerazzurri were close to becoming another big scalp for ambitious Catania, who took a rapid two-goal lead at the Stadio Angelo Massimino through goals from Gonzalo Bergessio and Giovanni Marchese.
Stramaccioni decided to take drastic action by making two substitutions at the break and one of his changes proved particularly inspired as Rodrigo Palacio completed a brace at the death, adding to Ricky Alvarez's strike for a 3-2 win.
The Nerazzurri boss told inter.it: "We started very badly, due in part to an amazing atmosphere here in Catania, and our opponents began very strongly.
"We made a huge mistake on their first goal and on the free-kick with 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."
Italy striker Antonio Cassano was conspicuously absent from the matchday squad and Stramaccioni decided to address questions about a reported changing room bust-up.
"There's training tomorrow [Monday] and Antonio will be there just like the rest of his team-mates," he added. "And we'll prepare for Thursday's game (against Tottenham).
"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 changing room is our business alone.
"These are all things that happen between men in a changing room."
Catania coach Rolando Maran, meanwhile, criticised his players for getting carried away and not anticipating the strength of Inter's desire to force a result in Sicily.
He told La Repubblica: "Our biggest mistake after the break was holding onto the ball too much and not realising Inter would come back at us.
"We were always looking to close out the match and even had a few chances to extend our lead again at 2-1.
"Inter really enjoyed themselves as they pegged us back but I really don't think we deserved the defeat. We have to accept the result."