The under-fire coach, who had gone three games without a win, saw Tommaso Rocchi earn the Nerazzurri a vital 1-0 victory which lifts them into fifth place in the Serie A standings
The coach went into the game at San Siro under intense pressure after a dismal run of form which had resulted in the Nerazzurri tumbling to eighth in the Serie A standings, as well as bowing out of the Coppa Italia in midweek.
However, Tommaso Rocchi popped up to score a crucial late winner against the Gialloblu which moves Inter back into the reckoning for a Europa League place and provides some welcome relief for their under-fire coach.
"For us it is a victory of great significance," Stramaccioni admitted to Sky Sport Italia in his post-match interview.
"We are always in an 'emergency', but with this performance the guys have given a great answer to everyone.
"To the president [Massimo Moratti], who always gees us up and did so again before the game, and to the fans, who are always behind us.
"We played a good first half and we knew that it could pay off in the second half. It happened when Parma had inserted some fresh faces. But, in the end, we managed to get a result and we are happy."
Stramaccioni refused to be drawn too much on his chances of holding onto his job, but did at least give his club's fans some cause for optimism by hinting Moratti is already busy arranging summer transfers.
"The team must concentrate on the remaining games, but I know that the president is already working on building a great Inter," the 37-year-old Roman revealed.
"But I have to think only of [our next opponents] Palermo, and the same goes for the team."
Inter now sit fifth in Serie A, two points behind Fiorentina, who have a game in hand.