The Argentine was confirmed as Tim Sherwood's successor at Tottenham Hotspur earlier this week.
"It's a blow for everybody to lose him, you can't really get away from that, and the players all loved working for him," Sky Sports News quotes Davis as saying.
"He pushed us on from where we were at before he came in - everyone personally improved, results improved as well and things were looking bright for the future.
"It's disappointing but at the same time I don't think it will affect the club in terms of progression because there is still a lot of growth left in the team."
Numerous reports have claimed that Southampton could face a player exodus following rumours that England international Adam Lallana and Luke Shaw are being touted by other clubs.