Adkins inspired the Saints to back-to-back promotions but was axed from his role on 18th January by chairman Nicola Cortese and was immediately replaced by former Espanyol boss Pochettino.
At that time, Southampton were three points clear of the relegation zone and have only moved one further point clear of the bottom three to sit in 12th place under Pochettino.
However, Davis, 36, believes Pochettino has provided the players with a new level of confidence, which is reflected in recent back-to-back wins over Liverpool and Chelsea.
"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," said Davis. "We are in a state of mind where we can feel we can win every game at the moment.
"There's certainly been a raising in player performance. The lads have reacted positively to it (his arrival).
"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."
On Saturday, Southampton travel to bottom club Reading, now managed by Adkins.
Davis is not surprised to see his former boss take up another post so quickly.
"I'm sure he wanted to get back into football as soon as he could, most managers that move on from a club want to stay in the game," he said. "From that side of it, it doesn't surprise me.
"We achieved a lot while he was at the club in a short space of time and the club is continuing to grow without him now."