Palace are now just three points ahead of Scunthorpe, who occupy the final relegation spot, after Saturday's 2-1 defeat by the Iron.
But the Eagles survived avoided relegation on the final day of last season and McCarthy insists they can repeat the trick, starting with a win against Doncaster on Friday.
"We're still in the driving seat, we have the character to survive," he said.
"It's up to us now to bounce back and take the game to Doncaster."
Source: PA
