Alvaro Negredo scored a hat-trick, Edin Dzeko grabbed a brace and Yaya Toure added another as City took a massive step towards the final at Wembley.
The result at the Etihad comes just days after the struggling Londoners crashed out of the FA Cup to Championship side Nottingham Forest and McCarthy admits his side were simply not good enough.
The Northern Ireland defender told the club's website: "It's just a disappointment all around. It's the semi-final of the cup and as much we tried to put the effort in, we just weren't good enough.
"Throughout the first part of the season, when you look at their home results, they've scored a lot of goals against Manchester United, Tottenham, Arsenal and Norwich.
"It's not as if it's the first time they've scored six goals at home. They're a very good team with great players and we found it very difficult on Wednesday.
"We certainly didn't play anywhere near as well as we can, but take nothing away from Man City, they were really good. Their finishing was exceptional."
McCartney is grateful for the support received from the travelling fans and says the players are determined to turn their season around as quickly as possible.
He added: "The players and the staff all appreciate the support the fans give us. They haven't had much to cheer about for the last few weeks but the lads are trying to turn that around.
"We're going through a difficult time at the minute and trying to come through the other end. The Premier League is very important and we've got a massive game on Saturday.
"It's not going to be easy [to forget about this] as defeats like that are hard to take. We need to move on to the Cardiff game on Saturday and we need three points."