Inter crashed out of the Coppa Italia after losing 1-0 to Rafael Benitez's men and Ranocchia shouldered much of the blame for his role in the late winner.
The Italy international, who has been widely criticised for his form this season, failed to react to a long throw-in and then fell over, allowing Gonzalo Higuain to run through and score in the third minute of second-half stoppage time.
Mancini vented his anger after the match, but the Inter coach is hopeful that Ranocchia receives the backing of supporters, insisting individuals are not to blame for the team's current plight.
"The fans have to trust me, that's the only way forward," he told reporters ahead of Sunday's clash with Palermo.
"We need results, though. We need balance – we need to not get carried away when we win or get depressed when we lose.
"There's never just one person to blame. You win and lose together. I think the fans will support Ranocchia.
"Something has to change, but I get the impression that we really are becoming a team."
The former Manchester City tactician is particularly wary of Sunday's opponents, reminding his players that seventh-placed Palermo are more than capable of causing Inter problems.
He was happy to report, however, that both Lukas Podolski and Rodrigo Palacio could be in line to return to the starting line-up.
"We'll decide whether to change anything around on Sunday. Podolski and Palacio are rested and fresh," he added.
"It is exactly the sort of match that could throw up problems. We'll have to play a perfect game."
