The 21-year-old signed a seven-year deal on Friday to swap the club he joined aged seven for Pochettino's new-look Stamford Bridge outfit.
The City academy graduate played 14 league games during the club's Premier League title-winning season last term and was an unused substitute as they beat Inter Milan to win the Champions League in June.
Despite his increased involvement in the champions' first team - which included scoring in both the Community Shield and UEFA Super Cup this season - his new manager hinted a chance to play a more significant role in west London may have been a factor in persuading him to move.
He becomes the club's 12th signing of the current transfer window, taking spending during the first 16 months of ownership of Todd Boehly's Clearlake Capital consortium over £1billion, but Pochettino said it is likely to be the last of the club's business before Friday night's deadline.
Mauricio Pochettino heaped praise on Cole Palmer after joined Chelsea from Manchester City
But the Blues boss insisted that the 21-year-old may need time to thrive at his new club
With so much player turnover and with the youngest average squad age in the league, he has stated repeatedly in the early weeks of the season that too much cannot be expected too soon and applied the same argument to Palmer's arrival.
IT'S ALL KICKING OFF!
It's All Kicking Off is an exciting new podcast from Mail Sport that promises a different take on Premier League football, launching with a preview show today and every week this season.
'I think he's a fit for the project,' said the manager. 'He's a young, talented player. He decided to come because he expects to play maybe more and be important here.
'But that's not the most important thing. The most important is that he sees Chelsea as a project for him, and to improve his game, and to be more involved every single game.
'The quality is there, there is great potential. Now he needs to settle here and prove and show that he's better than his team-mates, and that he deserves to play. He has to fight for his place.
'He's from Manchester and he's going to move to London. London is different, the club is different, the culture and everything. First of all, before he starts to perform, he needs to settle in his space and feel comfortable.
'We're not going to put pressure on him to perform (straight away). The most important thing now is to be happy and to find his space in the team.
'I think so (that is the end of transfer business). I think there's no time. If something is going on, I don't know. I didn't talk to my sporting directors since 11 o'clock (Friday morning). If something is going to happen they will communicate with me.
'We are happy with the squad. I don't believe that something will happen in the next few hours in terms of players in.'
The manager would not rule out the departure of Conor Gallagher, who has been the subject of a reported £40m bid from Tottenham.
The midfielder has started every game under Pochettino and captained the side in Wednesday's 2-1 Carabao Cup win against AFC Wimbledon.
'I think all the players that are involved in the squad are in our plan,' said Pochettino. 'After, it's a decision between the club and the player.
'Always from our side, Conor was a player that is consistent and can perform in different positions. We are so happy with him.
'He was captain against Wimbledon, he's an important player for us. What's going to happen in the future, I don't know, I cannot tell you this. It's like a player asks me 'how do you see myself in the future?' I don't know, I cannot know. It's up to you.'
Pochettino added that he could not rule out Conor Gallagher departing the club on deadline day
The manager added that he had been under no illusion that Romelu Lukaku would play a role with the first team this season.
The striker finally departed on Thursday on a season-long loan to Roma, having not trained with the squad since returning from a stay at Inter nor been given a squad number.
'I'm not disappointed because it was so clear the situation,' said Pochettino. 'I didn't create any expectation in my mind. The club was clear in the situation.
'What I heard from the club was the that the player wanted to leave. It was clear he was not going to be here this season.'
اخلاء مسئولية! : هذا المحتوى لم يتم انشائة او استضافته بواسطة موقع اخبار الكورة و اي مسؤلية قانونية تقع على عاتق الموقع مصدر الخبر : dailymail.co.uk  , يتم جمع الاخبار عن طريق خدمة ال RSS المتاحة مجانا للجمهور من المصدر : dailymail.co.uk  مع الحفظ على حقوق الملكية الخاصة بمصدر الخبر.