Spurs were denied back-to-back home Premier League wins by a resolute Palace side who came close to gaining three points when Jason Puncheon struck the bar late on.
A lacklustre showing at White Hart Lane came off the back of a comprehensive 3-0 defeat to Chelsea on Wednesday, just when Spurs looked to have turned a corner under Pochettino with wins against Hull City and Everton.
However, following Saturday's stalemate, Pochettino felt his side were hampered by a lack of rest following Wednesday's defeat at Stamford Bridge.
"We knew [Palace] are a very physical team and we didn't show the freshness that we showed against Everton.
"I think that [I am] not happy with the performance, the draw is fair. The team didn't show the freshness, maybe because we played in nine days four games or in six days three games.
"We play a lot of games and we are still young because we have a lot of young players but it is not easy.
"When you play Chelsea, when Chelsea have one day more for recovery, and then today you play Palace and you have two days for recovery while they have three.
"That is a little advantage the opponent has. We need to be more aggressive but today we had a lack of freshness."
Referring to the importance of having an extra day to recover, he added: "It's massive, but it's not an excuse.
"One day more is massive for the players but it's a tough competition and we need to understand the schedule is not good for us.
"Maybe in future it will not be good for another team. An extra day is very important for the muscles and maybe you need more than 48 hours but it's not an excuse. We need to accept that and improve."
