Samp lie 17th in Serie A ahead of Sunday's game at Fiorentina. Last weekend's 4-3 defeat against Sassuolo was the Blucerchiati's sixth loss of the campaign and piled more pressure on Rossi.
Rossi has delivered just two victories in 11 attempts this season but the coach has no intention to throw in the towel.
He explained: "Since I started doing this job, I have always felt under scrutiny.
"I have spoken to the club about our current situation and how we can come out of it.
"I believe I'm the right man to guide Samp and I feel that I have the support of the players and the club.
"Right now we are lacking balance and at times we play with fear and we must improve."
Samp will be nowhere near full strength as they have four players out injured while defenders Andrea Costa and Daniele Gastaldello are suspended.
A defeat could prove costly for Rossi, whose side are level on nine points with Sassuolo, who are in the relegation zone.
Rossi can expect a frosty reception at the Artemio Franchi stadium.
The Italian tactician returns to Florence for the first time since he was sacked by Fiorentina in May 2012 after he attacked player Adem Ljajic during a Serie A game.
Fiorentina go into the contest looking for a third straight win this week. The Viola followed their 2-0 at AC Milan with a 2-1 come-from-behind victory at Pandurii in Thursday's Europa League match.
The midweek result ensured Fiorentina qualified to the last 32 of the competition with two games to spare.
"It's not going to be easy but we want to win on Sunday," Fiorentina coach Vincenzo Montella said.
"It's going to be a delicate game because my players have had very little time to rest."
Giuseppe Rossi, who is Serie A's top scorer with nine goals, will lead Fiorentina's attack having rested in midweek.