Swansea boss Carlos Carvalhal reacted pragmatically to the defeat, saying: "We understand the difference between the teams, it is very clear. It's important to go to the semi-final and to have the possibility to fight for the trophy", Pochettino gushed after the tie at the Liberty Stadium on Saturday.
With Harry Kane out injured, plus the likes of Dele Alli and Mousa Dembele on the bench, Christian Eriksen was the star of the show as he scored twice, while Erik Lamela added another in a game Mauricio Pochettino's men dominated from start to finish as their final chance of silverware this season remains intact.
"We fully deserved the victory. We keep the same way, the same dynamic and that is so important".
In between Eriksen's sumptuous opener and Lamela's terrific effort on the stroke of half-time, Eriksen thundered the bar, Lucas missed from six yards and Eric Dier flashed a free header over the bar, while the video assistant also denied Tottenham what they thought was a legitimate goal. For Swansea the challenge is to stay in the Premier League, having clawed their way out of the relegation zone.
But Tottenham were unruffled and quickly settled into a tempo that had the home side outnumbered and second best in midfield.
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Canadian plane maker Bombardier said it was sending an air safety investigator and a field service representative to the site. The latter responds and says "We would like to land on 20"; he is cleared to land on that end of the runway, the report said.
The hosts rallied after the break and visiting keeper Michel Vorm had to be at his best against his former side to keep out efforts from Martin Olsson and Tammy Abraham.
Eriksen is lethal when given time and space and he had both in abundance as he advanced before curling a left-foot shot past the dive of Swedish keeper Kristoffer Nordfeldt.
But the victory was not without controversy as, with Spurs 1-0 ahead, Heung-Min Son's 23rd-minute goal was ruled out for offside.
Once again, Swansea were chasing shadows and when Sissoko played in Lamela the Argentinian skipped past Tom Carroll and calmly passed the ball into the corner of the goal before Nordfeldt had time to move.
The Spain worldwide striker, who earns £75,000 per week as salary at Spurs according to Spotrac.com, came on as a substitute in the 73rd minute. The visitors' third goal came after a long spell of possession when Eriksen arrived on the edge of the area to thump a shot past Nordfeldt who was deceived by the bounce.