The Rams missed a penalty at Pride Park as Town sneaked six points clear of the relegation zone with just five games remaining.
McCarthy said: "We burgled it. I thought I heard the sirens and I said 'shut the doors, the police are coming!'
"And we didn't deserve three points on that performance because they were better than us.
"We saved a penalty and had to stick at it because we've not played particularly well, but it was a bit of quality at the end - a great strike.
"He's 34, Carlos. He's stayed on the pitch and ran his socks off and then produces that.
"Derby have played well at times and they were the better team.
"We worked hard, we've fought our corner and we got lucky today. But that spirit has been right through the club since I've been here and without that we'd have been out of the league now. They deserve a huge amount of credit for that."