The attacking midfielder was subbed off when they were 2-1 up against Sheffield United in the Premier League on Sunday.
However, the Blues ended up conceding a late goal and drew 2-2 against the bottom team in the league.
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Asked about subbing Palmer due to injury, Pochettino responded: "No, no, no. I think he was tired.
My feeling was he was tired. 2-1 for us, Carney is another No.10 who can play there and do the job.
Yes, I think we are happy with him. We need to protect him. He got a knock against Manchester United and was a little bit more tired than normal, but we wanted to protect him after scoring the second goal.
Trying to avoid a problem for the future."