Saints six-match winning streak at home came to an end with Tuesday's goalless draw against leaders Brighton.
But Davis is confident they can see off their League Two opponents and book their place in Sunday's third-round draw.
"It's another home game and it's a game we can win," he said.
"We feel we can win every home game and the fact we spoke about the disappointment of not winning against Brighton shows we've got the mentality to win which we've been looking for, and we want to keep it until the end of the season."
Source: PA
Source: PA