"It's a difficult result to swallow and we'll have some psychological work to do as so often happens when a coach takes over," the 52-year-old said as he was officially unveiled on Tuesday. "There are problems everywhere but I'm sure I'll be managing a side with bags of quality."
Cosmi, who is Palermo's 13th coach since president Maurizio Zamparini bought the Sicilian club in 2002, wants a place in Europe next season for the eighth-placed team and success in the Italian Cup in which they play AC Milan in the semi-finals.
"The president Zamparini is a person who wants to take the club forward," he said. "He's told me the goal is the Champions League."
Earlier, Delio Rossi paid an emotional farewell at a news conference in Sicily to his former players and the fans with whom he said he "built a relationship based on mutual respect.
"Coaches and presidents come and go but there will always be a Palermo," he added. "Everybody knew the game was over. It was just a matter of when."
Delio Rossi took over from Walter Zenga in November 2009, leading Palermo to fifth place in Serie A within two points of a Champions League place in their most successful season ever.
But after Sunday's 7-0 hammering, in which Palermo suffered their third straight defeat after finishing the match with nine men, Zamparini exploded.
"The team is broken. He's ruined my Palermo," said the club owner despite their relatively healthy league position.
Without referring to Zamparini directly, Rossi defended himself.
"I don't mind criticism of my tactics but one thing I will not accept are personal attacks. I have my dignity," he said between tears. "Thanks to everybody. Don't you cry too. It will only make it more difficult than it already is."
