The Argentine announced on Thursday that he had agreed a new contract with Spurs that will leave the 46-year-old at the club until at least 2023.
The news also came as Pochettino moved to insist that the Lillywhites will now have to "take risks" in order to challenge at the top level of European football.
"Yeah, I can understand what he's saying [about taking risks]," said Davies, according to the Evening Standard. "Now it's all about trying to reach that next level and, as players, we want to do the same.
"That's great news for us as a club and it's fantastic to see him staying on. He's been amazing to work under and it's nice to see that continue."
Pochettino led Spurs to a third-place finish in the Premier League season, while Tottenham also produced an impressive display in the Champions League before being knocked out by Juventus at the last-16 stage.