Spurs conceded first when Alberto Paloschi scored his first Premier League goal for the Swans in the 19th minute at White Hart Lane before Nacer Chadli and Danny Rose scored within seven minutes of each other in the second half to give the North Londoners a 2-1 win.
Tottenham had a remarkable 14 shots on target throughout the contest and although they eventually came up with two goals, Pochettino felt it was going to be a disappointing day such was the performance produced by Swans keeper Lukasz Fabianski.
"During the whole game we shot more than 30 times and maybe 15 or 16 on target," Pochettino said.
"Maybe it was a record for the Premier League. Fabianski was fantastic and it looked like it would be impossible to score.
"For that you get upset, disappointed, frustrated a little bit but when we scored the second goal you feel freedom in this moment."
The win keeps Spurs two points behind league leaders Leicester City with 11 matches remaining.
Tottenham next take on London rivals West Ham United at Upton Park on Wednesday night.