Chelsea completed their £42.5 million deal to sign the 21-year-old on the final day of the summer transfer window.
Palmer made just 19 Premier League appearances during his time at City and has joined Chelsea with a view to secure regular minutes this season.
However, Pochettino is adamant that Palmer did not receive assurances before deciding to swap City for Chelsea.
‘If someone guarantees to some player to play ok, that is not the case here,’ Pochettino said.
‘The player needs to come and to perform and let us manage. And then if he deserves to play he will, I am sure it was the same at City. But for us even when you pay big money for a player at Chelsea it doesn’t mean you are guaranteed to play. That is the wrong way to think.
‘People need to learn about that. When we sign a player we do it for them to be part of the squad, involved in the squad, be part of the club. Be part of the dynamic. We never sign players who we promise will play. It has never happened, even when we signed Messi at Paris Saint-Germain.
‘I would never promise then they will play 20 or 30 games. Come on, that is very disrespectful to the player and to the environment you create here. You have to show that you are better than your team mates.
‘That is why we have 24, 25 players. It is the wrong way to think to move somewhere because you are going to play more. If someone promises you are going to play, ok, but that is no good for anyone.
‘Players cannot feel too comfortable. Players need to feel always under pressure to deliver the best. They need to feel that they have to show their best to play every day. It is the only way to improve. They are not stupid and they know when they are going to play but they need to keep pushing, pushing, pushing. If they go to sleep and think they will always play, then the wrong thing has happened.’
When asked about Palmer’s best position, Pochettino said: ‘He has the quality to play between the lines, No. 10, playmaker.
‘He is a player who is different to the players we have. He can play on the side, left or right. He can play one-v-one and go inside and link with the play.
‘Then he can also play as a No. 10 as he has the quality. He also can play No. 8 as he has accuracy with his passes.’
For more stories like this, check our sport page.