In the end it was comfortable, as Tottenham Hotspur ran out 3-0 winners over Tamworth. Ultimately in extra time, fitness, stamina and Premier League playing resources did the business over the National League part-timers. All that matters, their manager Ange Postecoglou was keen to point out as he conducted his post-match media duties in the corner of the Tamworth pitch, a gaggle of home supporters doing their best to get as close as possible to the visiting celebrity, is that Tottenham are through to the fourth round.

But how Spurs toiled for so much of this tie. For 90 minutes their side of internationals was bettered by Tamworth’s collection of electricians, fitness instructors and labourers, a team brilliantly organised by their teaching-assistant manager, Andy Peaks. “Challenging” Postecoglou called it. Others might have another term for the manner in which his team managed to play down to their hosts’ level for the bulk of the game – embarrassing, perhaps.

“We were not good enough for 90 minutes,” admitted Archie Gray. “Quite a few of us were not at the races today.” He was right there. Indeed, here was the perfect exemplar of how the Football Association has casually squandered one of the finest assets its competition once had. For Tamworth, flying into every tackle, charging into every confrontation, straining at every sinew, were magnificent for 90 minutes, keeping their Premier League guests comfortably at bay.

In the past, their efforts would have delivered a replay at the Tottenham Hotspur Stadium that would have given the club financial stability for a couple of seasons to come. They had worked their socks off, indeed came within a mishit shot of winning it. But instead of a proper reward, extra time loomed. Postecoglou was able to send on reinforcements of the quality of Son Heung-min and Dejan Kulusevski. Fitness told, Tamworth folded. And the dream was over.

For those looking for ways to maintain some sort of romance in the FA Cup, this game also offered convincing evidence that, in the third round at least, when a lower-division side draw Premier League opponents, they should be gifted a home tie. After the damp squibs of Goliaths against would-be Davids at the Etihad and Anfield, this was one of those events that really underpins the competition’s point.

An hour ahead of kick-off, Tamworth’s tiny Lamb Ground was already packed. In the Shed, the claustrophobic, low-roofed terrace holding the home fans that runs down one side of the ground, the chance to watch players of a level rarely if ever seen in the flesh was being relished. Humour was everywhere. “How s--- must you be, you’re sat on the bench” was the chant that greeted the Tottenham substitutes as they sat, immediately in front of the stand, on a row of chairs purloined from the bar.

And their good cheer was not diluted as the game began. It was reinforced. Their goalkeeper Jasbir Singh, the hero of their penalty shoot-out victory over Burton Albion in the previous round, appeared determined to play the opposite of Angeball. Every time he took a goal-kick, there was no pass sideways to a nearby defender. Instead it was launched high and hard, in the hope that the sizeable, elbows-out centre-forward Dan Creaney might create some chaos. Alongside him, the quick, jinking Beck-Ray Enoru caused Spurs’ jittery backline all sorts of problems with his direct running.

Even as the Tamworth team were enjoying the moment of their lives, the Spurs players looked as if they wanted to be anywhere but here, playing on an artificial surface against such motivated opponents. And when midfielder Tom Tonks slung in the first of his not-so-secret-weapon long throws, panic ensued, every Spurs player including goalkeeper Antonin Kinsky missing it as it crashed against the post.

And so it continued, Spurs players were second to the ball, pulling out of challenges, in Timo Werner’s case looking as if he might be lucky to get a game for Tamworth. When he missed a straightforward chance by allowing Singh to beat away his lame shot, the 800 Spurs fans crammed into the away section must have feared for the worst.

Especially when, with seconds to go in normal time, Tamworth missed the chance of the game, the stalwart centre-back Jordan Cullinane-Liburd mishitting his shot when the ball arrived at his feet from a late, late corner. All around the ground, the home supporters held their head in their hands, knowing that might be the chance of glory spent.

So Spurs staggered into extra time. Postecoglou was able to send on the cavalry and, firstly, an own goal by Nathan Muya Tshikuna, then sharp finishes from Kulusevski and Brennan Johnson delivered the expected result.

“I asked my players to give me everything,” said Peaks. “And they did that. I’m so proud of them. I hope they will remember this.”

In truth they deserved more than praise. They should have been granted a lucrative replay, an opportunity to enjoy themselves in the finest stadium in the country. Instead they next face Boston United in the National League. You suspect it will not be quite the same.