Spurs sit 71 places higher than Newport in the league pyramid but fell behind at Rodney Parade when Padraig Amond rose highest to head home Robbie Willmott's cross late in the first half.
82' - GOAL! Newport 1-1 Tottenham (Kane): Spurs have the equaliser, and who else but Harry Kane who nets his 30th goal of the season.
Spurs will not play in a situation like this again anytime soon - there will not be many League Two teams left in the fifth round, if they get there - but Pochettino still wants his players to learn.
With their next three league games pitting Spurs against Manchester United, Liverpool and Arsenal just a matter of days before they resume their Champions League campaign with a trip to Turin to face Juventus, an additional game is surely one that Pochettino could have done without.
"If you fight from the beginning of the game you can show your quality".
An ignominious exit loomed for a reasonably strong Tottenham outfit but, with the visitors seemingly fast running out of ideas, substitute Son Heung-min flicked on a corner and Kane ended a frustrating night in front of goal with the simplest of far-post tap-ins.
This time he had to introduce the South Korean from the bench, as well as bring on England midfielder Dele Alli, in order to turn the tide.
Pochettino: "There is a lot of rumours about different players".
"I didn't say we weren't motivated, but not motivated in the same level as Newport". "We lost every challenge in the first half".
Newport County manager Mike Flynn was left frustrated after their 1-1 draw with FA Cup opponents Tottenham.
With the club now building a new 61,000 seater stadium, there are exciting times ahead but they can only be realised if the manager not only keeps hold of this current crop of players, he has to add to them too.
"I could have been selfish and tried to be the hero and gone for it (a win) but I would never jeopardise the finances. We will see what happens in the last few days".
"It's incredible, I'm proud of everything we've achieved. I don't get carried away, I keep my feet on the ground".
The 27-year-old was the standout performer in the first half with his neat passing and tough tackling, only for a 32nd-minute booking to put a brake on his excellent display. Moving to the London club was seen as the player's "imminent destiny".