The Nerazzurri had lost four of their last five games and, with up to 13 senior players missing, Stramaccioni found himself under increasing pressure to turn things around at San Siro.
But a late goal from veteran striker Tommaso Rocchi finished off a resilient Parma side to earn Inter three points and a return to fifth place, with their coach now demanding a grandstand finish to the season.
He told inter.it: "It's a win that means a lot, most of all for my players. I'm proud to be the Inter coach and I'll give my all until the very end.
"The president (Massimo Moratti) came into the dressing room before the game and fired us up, which was great.
"A full-strength Inter is the only team to have beaten the top four teams. I was the coach then and the players were the same ones we have now."
Stramaccioni and director of sport Marco Branca have faced particular criticism for failing to recruit adequate cover for injured first-team players and signing under-performing winger Ezequiel Schelotto in January.
The former Atalanta man was the target of cat-calls and whistles from the Inter faithful as he hacked at a series of half chances while time ticked away in Milan.
"The banner protesting Branca? The fans have the right to express what they feel," Stramaccioni added.
"Schelotto's shin was practically knocked out of place after the contact with (Yohan) Benalouane. Any other player would have come off, but he stuck it out on the pitch.
"That shows his dedication to the team's colours. Quality wide players make for more spectacular football."
Parma, meanwhile, are drifting towards mid-table obscurity having won just twice in 14 games to tumble out of the race for Europe.
Gialloblu boss Robert Donadoni told fcparma.com: "We must not think that the season is already over because that would mean going into the last matches and wasting all the good work we have done.
"We need to take responsibility for ourselves, starting with me, and rediscover the hunger and mentality that we had three months ago.
"We are lacking ambition and what we are doing just isn't enough. We are not yet safe from relegation and we need to react quickly."