Spain striker Soldado unwittingly diverted Ross Wallace's free-kick goalwards as Burnley plundered a two-goal lead in seven minutes at White Hart Lane.
The 29-year-old laid on two assists as Spurs hit back for victory, but struck the bar with the goal at his mercy from point-blank range.
The £26million man's latest goal drought has now reached five games, but Tottenham manager Pochettino still believes "the goals will arrive".
"In football you don't need to apologise, because we are sorry for him because I think he deserved a goal," said Pochettino.
"But in football the actions, maybe it's difficult to explain, but I am happy with his performance and his attitude on the pitch.
"All he needs to do is to try to be the best he can in every training session, and the goals will arrive.
"Always it's a tough period for a striker when he doesn't score, but I am very happy with his performance, and he knows that we support him.
"We can talk about different things but for me the most important thing is that he always fights and tries to do his best.
"His attitude was perfect; he was only missing a goal.
"But in football when you work hard, when you try every day and try to give your best, rewards always arrive."
Marvin Sordell opened the scoring with his first Burnley goal in 13 games at the club, before Wallace's heavily-deflected free-kick rocked Tottenham further.
Paulinho halved the deficit in the 10th minute, with Tottenham moving level on the stroke of half-time with Etienne Capoue's 20-yard drive.
Vlad Chiriches and Danny Rose claimed quick-fire goals after the turnaround to cement Spurs' path to the fourth round and a home tie against Leicester City on Saturday, January 24.
Soldado has scored just four goals in 23 Spurs appearances this term, contrasting starkly with Harry Kane's 17 strikes.
Emmanuel Adebayor did not feature despite Spurs boss Pochettino toying with bringing the Togo striker back into the fold after a nine-week absence.
Pochettino claimed the former Arsenal forward still has a future at the club despite his recent lay-off.
"Yes, I explained last week, he's nearly ready for selection," said Pochettino
" He's training in the last few weeks; his training sessions have been very good."
While big-money import Soldado continues to be upstaged by homegrown talent Kane, Burnley boss Sean Dyche also backed Soldado to come good in front of goal.
"He was in the right place: I've no problem with my strikers if they miss when they're in the right place," said Dyche.
"I'm not bothered by mistakes if my players are in the right place."
Dyche was more concerned by his side's defensive errors that turned the game on its head.
"I don't know if we let it get away, they are a good side," he said
" But when you're 2-0 up and you make mistakes like we did, it will be tough
"It was just the details that really hurt us tonight
They supplied the details and we didn't
You can't get away with that as this level."
Burnley now face a blank weekend on January 24, but Dyche does not expect any far-flung warm-weather training jaunts.
"Maybe we'll go to Scarborough!" he joked
" Joking apart, I don't know what we'll do yet
"We'll have to decide beyond that
Who knows if we'll benefit from that rest, there's no guarantee
"There's no choice about it: we wanted to win, we didn't, so we move forward."
Source : PA
Source: PA