The newly promoted club, who are playing in Serie A for the first time in their history after winning Serie B last term, failed to win any of their opening seven top-flight matches, leading to speculation that Di Francesco may be relieved of his duties.
However, after a run of just one defeat in their last five league games, Sassuolo are now one place above the relegation zone - a position Rossi believes vindicates his decision to keep Di Francesco in situ at the Stadio Citta del Tricolore Reggio Emilia.
"Every chairman would be tempted to sack the coach, but it wasn't our case," he said.
"We appreciate Di Francesco both as a person and as a football manager, for he was on the top of Serie B last season from the very first match day.
"It would have been a pity to fire him only after four matches (which garnered zero points and included a 7-0 home defeat to Inter), but now we have turned the corner.
"Sometimes, when a team is in trouble it's not the coach's fault - the squad and the board play a crucial role too.
"We are aware that we'll have to struggle until the end of the season."
