Interim manager Liam King said Gainsborough Trinity would have to take the disappointment of not making the play-offs on the chin after last-day heartbreak.
Title-chasing South Shields, who eventually finished second, won 1-0 at the Northolme to deprive the Holy Blues of a place in the top five.
Play-off rivals Buxton, who had started the day ahead of Trinity only on goal difference, were held to a 2-2 draw by Warrington.
But Trinity were unable to find the win that would secured them the final play-off place in the Evo-Stik League.
“If we had won we would have made it, but it is just one of those things,” said King, who was appointed until the end of the season alongside Ross Hannah after Lee Sinnott was sacked in February.
“If we hadn’t had the points ‘deduction’ (when North Ferriby folded) we would have made the play-offs.
“Since Ross (Hannah) and I came in we would have done enough to make the play-offs without the points ‘deduction’. But it is just one of those things. We will have to take in on the chin and move on.”
Trinity failed to exert any pressure for an hour and rarely looked like scoring.
Ben Hughes, who got his first Trinity goal in the Easter win at Grantham, went close with a run and shot early on.
After a goalless first half Alex Simmons might have given Trinity the lead, but after he fired wide Carl Finnigan gave South Shields a 62nd minute lead.
Four minutes from time Hughes’ fine shot was well saved.