Walker ended his eight-year stint with Spurs last month and became the most expensive English footballer in history after moving to the Etihad Stadium in a deal that could eventually be worth a total of £53m ($70m). His status as the priciest defender ever lasted just a matter of days before being assumed by another new City full-back in the shape of Benjamin Mendy.
"He's one of the best full-backs in England and Manchester City have paid a lot of money - £50m - just like they have signed different players to try to get success in the future," Pochettino was quoted as saying by The Mirror.
"But, for me, I think we have seen the best of Kyle with Tottenham. We helped him improve and learn. When you pay this type of amount for a player, it's because he's top and because you are at your best.
"Then it's normal that he will succeed. It's a big pressure because when you pay for some players, the pressure to perform as well in every game becomes greater.
"It will be different, the pressure, for him. But there is no doubt that he is a quality player, a talented player. And there is no doubt that he will succeed with Manchester City."
Pochettino also refuted any suggestions of a rift with Walker, who made 229 appearances for Tottenham after arriving at White Hart Lane from Sheffield United back in 2009, reiterating that he felt it important to head back north in pursuit of a new challenge.
The Argentine was originally said to harbour long-running doubts regarding the player's fitness and ability to play two key matches in the same week. The latter point was evidenced by Pochettino's decision to omit him from his starting 11 for the FA Cup semi-final clash with Chelsea and a north London derby against Arsenal in favour of rival and fellow England international Kieran Trippier.
Walker faced a swift reunion with his old teammates in Tennessee last week and was booed by sections of the Tottenham support during a 3-0 International Champions Cup loss to City at Nashville's Nissan Stadium. Pochettino said after the match that he totally understood the fans' reaction, but did not think it was personal.