Walker made his move to Manchester City last summer in a world-record £53m deal for a defender, giving Trippier his chance to make the right-back slot his own after signing for Spurs from relegated Burnley for like £3million in 2015.
Trippier enjoyed a successful season last year under Pochettino, contributing with five assists, and earning a call-up to Gareth Southgate's England squad for this summer's World Cup in Russia.
The 27-year-old enjoyed a brilliant campaign in Russia, becoming only the third Englishman to score in a World Cup semi-final when he curled a free-kick into the top corner during the defeat to Croatia.
Pochettino feels his coaching team unearthed a gem when signing Trippier, telling reporters: "Sometimes things happen, sometimes you’re lucky and of course when we signed Kieran, we were trying to challenge Walker.
"We improve them and give them better tools to improve, but sometimes we need luck too and he deserves the credit because he made the effort to improve and step up his career."
Serge Aurier started on the opening day win over Newcastle, with Trippier having returned to training just five days earlier, and Pochettino says a long and demanding season means competition is vital for his squad to keep improving.
Pochettino continued: "It’s not easy but I said before, it’s difficult because at full-back we have young players, but yes, sometimes you need to take decisions and I am happy with the squad.
"We feel to perform and keep the same level you need players that need to wait for their opportunity.
"There are a lot of games to play and the Premier League is so competitive, injuries, tiredness, if you compete in the Champions League and cups, I think international games too it’s important to have a competitive squad."