That followed on from a 2-1 defeat to Chelsea before being held by Burnley.
"Very disappointing because we did everything to win". We created lots of chances and deserved more.
Pochettino said: "I am happy with the performance but disappointed with the result".
Alli, in particular, found it hard to find space between Swansea's two compact banks of three and struggled to move the ball quickly enough when gaps did appear; Son and Kane drew smart saves from Fabianski but Spurs' approach play was ponderous and telegraphed. They dominated every area of the pitch for the full 90 minutes, outshooting their visitors by almost a factor of four while registering eight shots on Lukasz Fabianski's goal.
But Pochettino's side were becoming increasingly frustrated, never more so than when a strong handball claim against Martin Olsson was overlooked by referee Mike Dean. "It is so clear".
Serge Aurier should have been awarded a penalty in the final minutes when tripped by Jordan Ayew but referee Mike Dean wrongly adjudged the Ivorian had handled during the build-up.
It could prove a different story this time around but Pochettino, the Tottenham manager, said: "It's frustrating and we need to do better".
Swansea manager Paul Clement praised his side who he felt may have provided the template for visiting teams at Wembley.
Clement was proud of his side's performance, and says succeeding with a defensive approach should be praised. Renato Sanches was chased by multiple big clubs before signing with Bayern Munich after he won Young Player of the Tournament at Euro 2016. It helps that he has the likes of Alli and Eriksen alongside him, and if those two can provide Kane with the chances that he is a master at putting away, Spurs are sure to be lingering around the top of the Premier league table.