Ange Postecoglou’s Premier League giants were taken to extra time by their hosts after the initial 90 minutes ended in a 0-0 draw.
Tamworth did their fans proud as they brilliantly kept a clean sheet in normal time while also recording 13 shots of their own.
But Spurs’ might and squad depth paid dividends later on when they took the lead through a 101st minute own-goal from Nathan Muya Tshikuna.
Dejan Kulusevksi then made it 2-0 six minutes later.
And Brennan Johnson sealed an emphatic 3-0 win for the visitors with a goal at the death.
However, many fans feel Tamworth were denied a proper reward for their efforts in the normal 90.
Old FA Cup rules meant a draw between sides in that time resulted in a replay.
Had those still applied today, it would have seen Tamworth travel to London for a money-spinning adventure at Spurs’ £1billion stadium – which holds 62,850 compared to their Lamb Ground at 4,000.
FA Cup replays were scrapped only in April last year following a scheduling agreement with the Premier League.
And taking to social media, fans blasted the “cruel” change that denied the Staffordshire side their time in the sun.
One said: “Tamworth grafted for a 0-0. A replay would see them right for five years, but because the big boys get tired, replays are scrapped.”
Another declared: “The FA and Premier League has taken away the glory of a replay for Tamworth, it would have meant so much footballing wise and financially.”
One noted: “Tamworth not getting a replay which would likely bank them £1m is all wrong.”
Another added: “Robbing the players of their small piece of fame and robbing the local clubs of ££.”