The Rosanero are facing a return to Serie B after nine seasons in the top flight and a run of 13 games without a win leaves Gian Piero Gasperini's men five points shy of safety.
Victory over fellow strugglers Siena would put Palermo in pole position to catch 17th-placed Genoa but Dossena knows that will only arrive through a concerted team effort.
He told La Repubblica: "It's time to stop doing the maths and worrying about the table, the only thing that matters against Siena is winning.
"We just have to go out there and do what we haven't managed to do for a while, which is bring all three points home. We've made a lot of effort and thrown everything at it so far but it hasn't been enough.
"It's not always the case that when you concede goals it's the defence's fault, as it's not always the strikers' fault when you don't score them. It's the responsibility of the whole team.
"Each one of us has to take responsility and we must, in any which way we can, through good luck, through a bit of craftiness, get all the defenders, strikers and attackers in the best shape to work hard towards getting some goals."
Gasperini has returned to the bench at the Renzo Barbera after a three-game absence, with Alberto Malesani's brief tenure ending last week, and Dossena believes the former Inter Milan boss' fluid style will pay ultimately dividends across the 11-game season run-in.
He added: "He's a coach who likes the ball played on the ground, he doesn't like long balls, and he wants the whole team to conform to his style of play.
"When I've talked to former team-mates and other people who've watched us they've said that we don't play like a team in our position.
"Clearly we're just missing that little bit of luck to turn games in our favour. We have to put more heart and soul into our play."
Edgar Barreto, Abel Hernandez and Andrea Mantovani miss out against the Bianconeri as Palermo try to avoid drawing five games in a row for the first time since late 2007.
Midfielder Simone Vergassola is Siena boss Giuseppe Iachini's only injury concern with the ex-Sampdoria coach still cursing the six-point deduction issued in pre-season for alleged involvement in match-fixing.
He said: "I'm not worried about being joint last in the table because we have not really earned just 21 points but 27. That must give the team the desire to boost our position in the league table."