Saints moved above the Potters and Liverpool thanks to the 2-1 win at the Britannia Stadium on Saturday, with Ronald Koeman’s men now sitting seventh in the Barclays Premier League.
And after picking up the win at Stoke, Davis says Saints were well aware of the importance of the two games before the international break.
“We looked at the two games – this game and the Liverpool game before the international break as being very important in terms of where we see our ambitions for the season,” Davis told reporters after Saturday's win.
“We’ve taken the first step in the right direction and it’s about trying to keep that consistency going.
“It’s so hard to judge this season. We’ve gone through spells where we’ve been unstoppable and put together some great results.
“Then likewise we’ve gone the other way, when we’ve gone through times when we can’t manage to get a win.”
With victory in the first of two big games for Saints, Davis is now looking forward to welcoming Liverpool to St Mary’s on Sunday.
“It will be a good game. They’re in form. I watched them against Manchester United in the Europa League the other night and they played some excellent stuff,” added Davis.
“We know we’ll have to be at our best to get something from the game, but with the game being at home we’re confident we can show our quality and get the right result.”