The Hammers end the year on a low with the team languishing in 19th place following the 3-3 draw with West Brom at Upton Park on Saturday.
A dismal run of six league games without a win has left Sam Allardyce's side in a relegation dogfight, but McCartney believes morale remains high in the squad.
"You look over the last few weeks at the teams that have sacked their managers," said the defender. "The players haven't been happy with whatever way they were playing but our dressing room is great, confidence is high, the spirit is high.
"We're all in it together and we're still doing all the right things on the training ground.
"It is after Christmas now and when you find yourselves in the bottom three, everyone maybe gets a little bit edgy and games you feel you should be winning you're just not getting across the line.
"It eventually catches up on you. The dressing room's great and we're just trying to move up the table again and get ourselves out of this situation."
West Ham have been hampered by a shortage of centre-backs as Winston Reid, James Collins and James Tomkins are all nursing injuries.
McCartney was moved from full-back to the heart of defence at the weekend and he believes modern day players should all be versatile.
"I wouldn't say it was daunting," said the 32-year-old.
"I've played centre-half before in my life, I started out a centre-half and I've played international football as a centre-half and I know what's required.
"Obviously it's not great when you have two or three regular centre-halves out injured, but I think nowadays players have got to fill in when needed.
"We finished the game [against West Brom] with four full-backs in defence. It's required these days. You've got to be able play in more than one position and fill in when players are injured or when the manager needs you to do a job.
"So, it wasn't ideal to finish the game with four full-backs in the defensive slots but there was no other choice."