Lee Ashcroft’s players had gone into last Tuesday’s FA Cup tie with Skelmersdale United knowing victory would see them into the final qualifying round.
However, it was to be the visitors who progressed after a 1-0 win at the Mike Riding Ground.
Both sides had early sights of goal with Town’s Scott Harries shooting off target and Lloyd Ellams heading over at the other end.
Town keeper Lee Dovey made a fine double save while Dan Gray sent an effort off target and Tom Ince came close to scoring for the home side.
Jack Anderton and Owen Watkinson were also off target for Town, who then conceded a penalty for handball.
Dovey ensured they remained on level terms, however, keeping out Danny Mitchley’s spot-kick.
They were handed another boost seven minutes before half-time when the visitors went down to 10 men as Josh Peet was sent off for a second yellow card.
Anderton missed a golden chance to open the scoring for Town, who also saw Gray denied by the bar before the break.
Though they were a man down, Skem continued to threaten with Dovey saving from Ellams’ volley.
Danny Wilkinson and Harries were off target before Skem were awarded another penalty on 72 minutes.
Mitchley was the player brought down and, this time, it was Emini Adegbenro who took the penalty, making no mistake.
Harries and Brandon Lee were denied an equaliser within seconds of each other as Town sought a leveller.
It was the visitors who could have doubled their lead when Mitchley hit the woodwork from close range.
Paul Turner came close to rescuing Town, only to be thwarted by Skem keeper Ben Barnes before the final whistle heralded Town’s exit.
Saturday then saw Town travel to Northwich Victoria, where they were beaten 2-0.
The first sight of goal came on nine minutes when Anderton beat his man and crossed for Harries, who headed off target.
At the other end, Dovey was called into action to save from Matty Clarke, Matty Birchall and Darrhyl Mason.
The home side then opened the scoring just past the half-hour when Clarke found Dave Sherlock and he sent an effort from distance into the top corner.
Anderton had a couple of efforts at goal for Town as they trailed at the break, only to fall further behind early in the second half.
Louis Potts and Joe Camozzi combined, the latter crossing for Ash Dunn to head home from close range.
Dovey prevented them from adding a third, denying Birchall and then keeping out Brandon Barski’s header from the resulting corner.
Town had made a double change at the break with Turner and Joe Melling both introduced but it was Dovey in action again, this time getting the better of Mason.
Watkinson could have pulled a goal back midway through the half but he was denied by the Northwich keeper.
That was as close as Town got for the remainder of the game as the home side played out time to take the points.