The Spireites parted company with Martin Allen on Thursday following the 4-0 home defeat to Solihull Moors.
They club are in the National League bottom four and have won only once since the second week of August.
Pemberton oversaw things on Saturday and there was a big improvement as they fought back to hold Hartlepool to a 1-1 draw.
The caretaker spoke to the Derbyshire Times after and said it doesn’t matter how long it takes to get the right man in.
"I want to be part of this club long term,” he said. “If you end up the manager you probably don't end up long-term.
"I've said just make sure you get the right person you need.
"If I can nick a couple of results so we don't have to panic into the situation, we're okay.
“If it takes a week, a month, I'm okay with that.”
On the game, he added: “There's work to be done, you can see that.
“The goal was a bit of a killer, that's just game management. A minute to go and we're a little bit dopey with the pass, which exposed us.
"When they get a kick in the backside, it's how they recover.”