With Sean O'Driscoll sacked as City's head coach in midweek, Pemberton saw his side fall behind to Jack King's header in the 33rd minute.
It was King's first of the season and was enough to separate the two sides, while Paul Gallagher and Bristol City's Karleigh Osborne were both sent off in stoppage time for scuffling.
Pemberton said he had no idea how long he would be in charge and insisted his side did not have any luck.
"If they tell me to take it for a week I'll take it, if they tell me to take it for a year I'll take it, that's what I'm doing," he said.
"The players are happy with that, the players were brilliant after what happened during the week.
"The support I've had from them has been great, as you've seen.
"A good guy lost his job this week, but I know he just wanted to get on with it so that's what we'll do.
"Whoever takes over is getting a group of players who work hard, I wouldn't be standing here and tell you if I didn't believe that there's good players and they've fought hard.
"They either haven't got the rub of the green at times and at other times we've made stupid mistake and shot ourselves in the foot.
"They stick together. They put their bodies on the line and there were some moments where they've thrown things into the box, but they've not created too many chances against us."