The Saints are on the verge of securing Premier League football for a second season as they sit in 12th spot thanks to Saturday's thrilling 2-1 win against reigning European champions Chelsea at St Mary's.
And, with a game up next against former boss Nigel Adkins' new club Reading, who sit at the foot of the table and appear to be doomed to an instant return to the Championship, the Saints have a chance to pull further away from danger.
However Northern Ireland captain Davis insists that nobody is taking their foot off the pedal until the Saints are mathematically certain of avoiding the drop.
He told the Daily Echo: "We are still so close and we won't get carried away.
"We take a lot of confidence from the results we've got recently but we've got another massive game again next week to concentrate on.
"To be honest I think we're safe enough in terms of the personalities in the squad.
"We all know what we have to go and give in each game to go and get a result and that's the way we are in the Premier League.
"We know what it takes to win games and we have to show that same desire in each and every game we've got."