Goals from Connor Wickham and former Spurs winger Andros Townsend settled the game at Selhurst Park, after which Pochettino offered no excuses for his side's below-par performance.
"It was a fair result," Pochettino told reporters.
"They scored and we didn't. I can't say anything about that.
"We can talk about possession and shots but if you don't score you don't deserve to win games."
Pochettino made eight changes to his side, with only Paulo Gazzaniga, Jan Vertonghen and Fernando Llorente retained from the side that lost to
Chelsea.
With Harry Kane and Dele Alli injured, and Son Heung-min travelling back from the Asian Cup, Tottenham lacked a cutting edge in attack as they squandered numerous chances to get back into the game, including a penalty that Kieran Trippier missed.
Pochettino said: "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.
"We're out of two competitions since Wednesday and we're disappointed."
Crystal Palace manager Roy Hodgson paid tribute to Wickham, who scored his first goal in over two years having endured a long rehabilitation from a serious knee injury.
"It's a credit to him," said Hodgson of the 25-year-old, who scored after nine minutes.
"For Connor to crown it with a goal is good news. He's worked hard to get where he is. I decided to rest
Jordan [Ayew] so he could play."
Palace went into the game on the back of league defeats to
Watford and Liverpool, and have games with
Southampton,
Fulham and West Ham on the horizon.
Hodgson added: "I don't think we needed anything to change our approach or confidence.
"We have three big games coming up."
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