Ronald Koeman's team will attempt to extend their superb run to 10 wins from their last 11 games in all competitions when they resume Premier League action at Hull City on Saturday.
Victory would ensure they maintain their hold on second spot and reinforce their standing as this season's surprise package.
And midfielder Davis is confident the club's run of outstanding results has generated a momentum that means they will head to the KC stadium brimming with confidence three days after setting up a League Cup quarter-final tie with third tier Sheffield United.
"The dream is silverware, but it is a long way away
We have to keep going, take each game as it comes and show the same sort of quality and desire we showed against Stoke," Davis said.
"We are not prioritising, every game we go into we want to try and win
You could see that in the manager's selection.
"We've got good competition for places at the moment, everyone is fighting for their place in the team.
"We have a lot of quality with the signings that have come in
It is a good place to be at the moment."
Saints manager Koeman is also confident there will be no hangover from the draining clash with Stoke.
"The players were a little bit tired because it was a tough second half
It was physical and there were a lot of fouls, but we had to handle that and finally won the game," he said.
"The feeling of pain is more easier to adapt to and go on when you are winning because it gives the team a good belief and a good spirit."
- Goalscoring threat -
Meanwhile, Tom Huddlestone has praised fellow midfielder Mohamed Diame for helping add a goalscoring threat to Hull's midfield.
Senegal international Diame, 27, has made a strong start to his career at the KC Stadium after signing from West Ham on transfer deadline day in September.
Diame has scored four goals in ten appearances, making him the club's joint leading goalscorer with Croatian striker Nikica Jelavic.
Diame has flourished as the attacking figure in a three-man central midfield combination with Huddlestone and Jake Livermore.
"As Mo has shown, he is unbelievable at nicking the ball back, intercepting things and putting people under pressure and if it does break, he's got the legs and the energy and technique to pop up with some vital goals," Huddlestone said.
"He's been a revelation since he's joined us.
"Myself and Jake perhaps don't score as many as we should but with the three of us in there, it gives one of us the licence to bomb on every time."
Hull are likely to field a similar starting line-up to the one that drew 0-0 with Liverpool last Saturday.
Scottish full-back Andy Robertson is fit to return but will have to settle for a place on the substitutes' bench as Robbie Brady impressed at Anfield.
After keeping a clean sheet against Liverpool Eldin Jakupovic, the Swiss goalkeeper, will start only his third Premier League match, with Allan McGregor and Steve Harper still to recover from respective shoulder and bicep injuries.
Source : AFP
Source: AFP