Mills is still awaiting his first point since he was confirmed as Tommy Wright’s successor.
The Steelmen suffered a ninth defeat from their last 10 Evo-Stik Northern Premier League Premier Division matches as Scott Allison’s first-half goal condemned them to a 1-0 defeat at Workington.
With Skelmersdale United claiming a 2-1 victory over Ilkeston, Corby’s latest loss saw them drop to the foot of the table.
They remain seven points from safety and Mills insists he knew how hard things would be when he took the job on at Steel Park.
“It’s not an easy time and we were involved in a very scrappy game,” the Steelmen boss said.
“But we didn’t create many chances and we conceded a goal that was preventable.
“I haven’t got a magic wand and I said when I came in that things aren’t just going to happen overnight, it’s going to take a lot of hard work.
“When I took the job on, I knew how tough it was going to be.
“I have to get on with the job at hand and all I can do is give it my best.”
Mills handed league debuts to recent signings Jamie Tank, Phil Trainer and Stefan Moore in Cumbria and he insists the Steelmen will continue their hunt for more new faces.
“Stefan had a couple of chances that he would have taken with a bit more match sharpness and that will come with games,” he added.
“Phil offers us an extra physical presence in the midfield and I thought Jamie did well.
“We are still looking at bringing in some more players to help us. We will keep looking to add to the squad, we still need to bring a couple in.”
The Steelmen’s Integro League Cup first-round derby at AFC Rushden & Diamonds, which was scheduled to take place at the Dog & Duck on Tuesday, will have to be re-arranged with Diamonds now facing a Buildbase FA Trophy second qualifying round replay at Lincoln United following their 3-3 draw at the weekend.