Adkins was sacked in January having guided the Saints to consecutive promotions up to the Premier League.
Having taken charge with the side in 15th place in the table, Pochettino has since lifted them up to 12th position.
"The manner in which he has come in and lifted the club to a new level shows it was a decision that's been proved right," Davis is quoted as saying by Sky Sports News. "We are in a state of mind where we can feel we can win every game at the moment.
"Mauricio and his staff have come in and communicated very well and everything they are trying to pull off the lads are soaking up and fortunately we are putting that into our performances."
Adkins and Pochettino come up against each other in the league on Saturday as Southampton travel to Reading.