Saints saw a mini revival abruptly ended by a 1-0 home defeat to Sunderland on Saturday, although they will spend Christmas outside the relegation zone. The loss also maintained a three-point gap between themselves and 16th-placed Aston Villa - something Davis is looking to close quickly, starting at Craven Cottage.
"In terms of Christmas, I think the games we've got are winnable," he told Press Association Sport, referring to the trip to Stoke and visit of Arsenal that follows. "We go into those games fully intending to set our stall out so we can win those games. That's what we'll ask of ourselves."
He continued: "Who knows if Dimitar Berbatov is the man to watch out for against Fulham. I am not sure if he has scored many this season, has he? He is a top class player but he is not their only player. He didn't play against us down here and we conceded two goals so they've got quality all over the pitch.
"They wouldn't have been in the Premier League for this amount of time if they weren't quality so we will obviously pay them respect, but it is about turning up on the day, performing and taking the three points."
The Sunderland game was Davis' second back in goal after being recalled to Premier League duty.
The 36-year-old has been a mainstay in the Saints side that rose from npower League One to the top flight but was dropped for four matches into the season, having conceded 14 goals.
Paulo Gazzaniga and Artur Boruc have both enjoyed stints between the sticks since and Davis is keen to hold onto his first-team berth.
"When you are used to playing week in, week out, which I have been certainly at this club over the past three or four seasons, it is always difficult," he said. "But I accept that you can't always have it your own way and that the right thing to do is to keep your head down and work as hard as you can.
"Obviously I looked at myself and what I was doing. I felt that in terms of where I was, I am 36, it is about maintenance and staying on top of yourself physically. I felt that if I stayed in good shape and carried on doing what I was doing my time would come again."