Goals from Connor Wickham and Andros Townsend were enough to secure Palace a place in the next round of the coveted competition.
Tottenham’s Kieran Trippier missed a penalty to get them back into the game, smashing it wide of the post.
And Pochettino spoke about his side’s exit in his post-match news conference - where he was asked about Tottenham’s lack of silverware in recent years.
“Again we’re going to have the debate whether a trophy will take the club to the next level. I don’t agree with it,” he said.
“It only builds your ego. The most important thing for Tottenham right now is to always be in the top four.
“We came from a crazy fixture schedule and we were forced to make some changes.
“This season is tough and it’s going to be a massive challenge for us. We knew it would be a tough season for us but not as tough as it has been.”
Trippier missed his penalty against Palace (Image: GETTY )
Pochettino has not won any trophies at Spurs (Image: GETTY )
Tottenham have now been knocked out of two competitions in four days, having lost to Chelsea in the Carabao Cup semi-final on Thursday.
The tie ended 2-2 on aggregate, but Spurs endured penalty shootout heartbreak at Stamford Bridge thanks to misses from Eric Dier and Lucas Moura.
Pochettino noted this, but was quick to lament his side’s fixture schedule this season.
“We’re out of two competitions since Wednesday and we’re disappointed,” the 46-year-old added.
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