Catania raced into a two-goal lead early on but were pegged back by a late Inter comeback.
Substitute Rodrigo Palacio scored twice in the last 15 minutes to guide Inter to victory, a result that Stramaccioni admitted seemed extremely unlikely at half time.
He told Sky Italia: "We got off to an absolutely terrible start, aided by the crazy atmosphere in the stadium. I do not know how many people would have bet on us at the break.
"Catania started well, while we made awful mistakes on the two goals we conceded. At a time like this, if the team did not have real grit, then it would've been incredibly difficult to come back from that.
"It is an extremely important victory, as it was earned against the form team in Serie A right now.
Victory at Catania lifts Inter to fourth in Serie A, just a single point behind city rivals AC Milan in third place.