"Results say differently and that's what we're judged on, but I'll keep fighting and will stay here until I'm told something different.
"But I expected more from the side at Newport, especially the second half."
Wrexham, one from bottom in League Two, travel to Barnet on Saturday as they bid to clamber out of the relegation zone.
"The players just have to keep fighting and go again," Carey, who has yet to win a game as Dragons manager, told BBC Sport Wales.