The game had the makings of a huge upset from the opening whistle as Tamworth more than held their own but the team of part-time players tired in extra time and were unable to secure one of the biggest shocks in the competition's history.
"We should be proud, we took a top-six team to extra time," Tamworth goalkeeper Jas Singh, whose day job is as a building surveyor, told ITV. "We had chances as well, that's the frustrating bit."
After a goalless 90 minutes, Nathan Tshikuna's own goal in the 101st minute at the Lamb Ground put Spurs ahead after Brennan Johnson had fired a low cross into the area.
Substitute Dejan Kulusevski doubled the lead when he latched onto a pass from Son Heung-min to shoot across goalkeeper Jas Singh and Johnson added a late third.
Tamworth gave their fans at a rocking Lamb Ground plenty to cheer when Beck-Ray Enoru - who works as a shop clerk - forced Spurs keeper Antonin Kinsky to make a diving save in the opening minute.
Before kick-off, Enoru had climbed on a teammate's shoulders to repair a gap in the net with a roll of tape as an Spurs manager Ange Postecoglou watched on chuckling and Tamworth's Tom Tonks, renowned for his long throw-ins, sent one clattering off Spurs' far post.
Tom McGlinchey and Jordan Cullinane-Liburd had excellent chances to notch a late winner for the home side which had manager Andy Peaks - who quit his day job as support worker to become full-time manager ahead of Sunday's game - holding his head in disbelief.
Singh, whose partner had given birth to a baby boy the previous evening, was excellent in goal, turning away several Spurs shots including a couple from James Maddison.