Spalding United remain in the play-off pack after their first defeat in September.
The Tulips are sixth in the Evo-Stik South ahead of this weekend’s home game with mid-table Chasetown.
Boss Chris Rawlinson said: “If Basford United get it right, they will win the league. But we are still in a group of other clubs who are just behind in the mix.
“If we play like we did at Frickley Athletic, we can forget all about those two defeats over the August bank holiday weekend.
“We can afford to lose 1-0 as long as we back it up with a positive result on Saturday.
“It’s all about ourselves and a certain way of playing at home.
It’s all about ourselves and a certain way of playing at home.Chris Rawlinson
“The winning goal came from a catalogue of errors on Tuesday.
“Jamie McGhee took too many touches but won it back and Nathan Whitehead’s pass was cut out.
“As they played the ball over the top, Adam Jackson stepped up when he shouldn’t have done and the striker was onside.
“We weren’t at the races in the first half, although Gary King and Jamie Jackson had chances.
“They looked a threat and caused all sorts of problems. Jamie will score goals when he gets his sharpness back.
“On another day, we would have got a 1-1 draw thanks to the second-half display.
“We didn’t do enough to win it but we had chances and intense pressure.
“The way they celebrated at the end showed how much Frickley knew it was a good win.
“Defensively, Ellis Humble and Neal Spafford dealt with Gavin Allott who is the best striker in the league.
“I couldn’t fault anyone, especially in the second half.
“Keegan Townrow came in for his full debut at right-back and showed why his parent club Doncaster Rovers think he will progress through the ranks.
“Brad Maslen-Jones came into the squad as a midfielder and he makes forward runs.
“I thought we had done enough to get a point. We would have been good value for it as well.
“We did everything apart from get the ball over the line in the second half.
“Last week, we defended like that with nine men and held on at the end to win at home to Lincoln United.
“Football has a habit of going the other way at times but I don’t think we did badly.
“Not many teams will go to Frickley and give them a good game with players suspended, injured or unavailable.
“The lads were annoyed and disappointed. But we will get stronger with players coming back in.”
Jordan Lemon and Jack Fixter are likely to return to Spalding’s squad on Saturday.
Maslen-Jones, Matt Varley, Conor Marshall and Jonny Lockie are all serving bans for red cards.