The Lionesses suffered a 2-0 loss to France in Nicosia.
Carney played the full match, with Moore an unused substitute.
Both of the French goals came in the first half.
It was the fourth game that England had played in the Cyprus Cup - they had won their three previous outings against Italy, Finland and Canada before the final defeat.
The tournament was effectively a warm-up tournament ahead of next month’s World Cup qualifier with Montenegro.