The Eagles skipper was the only survivor from the side which started Wednesday night's famous victory over Manchester United.
Barely 48 hours later Palace, without a win in their previous five league outings, were leading courtesy of Chris Martin's first-half strike.
But luckless defender McCarthy turned in a cross from Paul Green in the second half to send Derby home with a point.
It meant the Rams avoided a sixth straight defeat - which would have equalled their worst run since they crashed out of the Premier League four seasons ago.
Despite overhauling his side, Palace boss Dougie Freedman did put goalscoring heroes Darren Ambrose and Glenn Murray, substitutes in Manchester, in the starting line-up.
The dynamic duo could have put Palace ahead after a minute when Ambrose, whose 35-yard thunderbolt stunned Old Trafford, ignored the predictable cries of 'shoot' to tee up Murray, but the striker's drive was well kept out by Frank Fielding.
Owen Garvan was sent crashing to the floor by Gareth Roberts as he went for the loose ball but referee Andy D'Urso waved away Palace's muted penalty appeals.
Nevertheless, the hosts continued to press and got their reward after a quarter of an hour.
Peter Ramage robbed Jamie Ward and squared the ball to Martin, whose 20-yard shot spun off Shaun Barker to leave Fielding wrong-footed.
They may have stolen the headlines for their cup exploits but it was Palace's first goal in the league in precisely 500 minutes.
Ambrose did try his luck from 20 yards as half-time approached but Fielding saved low down.
Derby put in a dismal first-half performance and a long-range effort from Jeff Hendrick, which flew well wide, was the sum total of their contribution.
However, they almost drew level just after the interval when McCarthy had to clear Jason Shackell's goalbound header and Craig Bryson's follow-up hit Mile Jedinak.
Tamas Priskin also should have done better when he met a cross from Roberts but his tame header went wide.
The equaliser finally arrived in the 75th minute, with McCarthy's horrible mistake proving costly.
The Irishman clearly lost his bearings as Green's cross curled into the area and in sticking out a foot to clear, succeeded only in diverting the ball past Julian Speroni and into his own net.
It could have been worse for Palace but Speroni saved well from Green in stoppage time.