The match also signifies the club's last remaining chance of silverware in a disappointing campaign.
Only as recently as Monday did club president Massimo Moratti publicly absolve Stramaccioni of blame for recent results which have seen them drop to seventh in Serie A, nine points off the Champions League spots with six games remaining.
A lengthy injury list was instead cited by Moratti, which was added to on Monday with fresh problems for Walter Gargano and Yuto Nagatomo.
Stramaccioni stopped short of echoing that view, but has clearly taken confidence from Moratti's comments.
"We've had this injury crisis for a while now, we've never used it as an excuse and we won't start now," he said.
"In fact, I'm sure we've taken it as added motivation to get a result which some people think is beyond us."
Asked about Moratti's comments, Stramaccioni said: "He has faith in the whole club at the moment, not just the coach.
"We all need to give it everything, right down to the groundstaff. Then we'll see where we are, but I don't think my future will be decided by tomorrow's [Wednesday] result, but rather what I've done over the course of the season.
"Tomorrow's match is very important, but I don't think it will make or break the coach's future or decide other issues. The president has made clear to us that this is a bad situation, a storm, and we'll ride it out together."
Inter's problems make Roma the favourites on Wednesday night, but midfielder Danielle De Rossi - himself recovering from a sprained ankle - is not underestimating the opposition.
"They're having a hard time with injuries, but we cannot take anything for granted," he told novarachannel.tv.
"Apart from the very bad game against Palermo (a 2-0 Roma defeat last month) we are in pretty good form, the next round is in our hands."