Cross sustained a right AC joint injury late in Sunday's first quarter against St Kilda.
He briefly tried to return in the second term before being subbed out and McCartney fears the injury is serious.
"I don't think it's great," McCartney said.
"For someone as durable and tough as Crossy to just be taken out of the game straight away, he's a brave soldier and we're going to miss him.
"His first reaction to me was that he felt bad that he let us down, that he wouldn't be able to be out there and help his teammates, which says much about what sort of person Daniel Cross is."
The 76-point defeat was the Dogs' sixth straight, most by big margins.
McCartney said a side with as many youngsters as the Bulldogs would struggle at times against more experienced opponents, but could not tolerate patches such as a run of nine unanswered goals from the Saints.
"That's what's been unacceptable, that a bad five minutes is turning into a bad 45 minutes," McCartney said.
He said physically immature players could not afford to let being shoved out of position by stronger opponents affect the way they attacked following contests.
McCartney suggested young key forward Liam Jones, who kicked 19 goals in 20 senior games last season, when he was named the club's most improved player, was one who needed to battle harder through a down patch.
This year Jones has nine goals from 12 games and managed just one kick, no marks and no score against the Saints.
"Sometimes when you're not playing the way you should, the one thing you should do is keep working and presenting and giving the team something.
"There's no doubt if you keep persisting and having a crack at the ball and working and making things more difficult for your opponent the game rewards you.
"If you don't, you get what (Jones) got today, you get not much at all."