The Tigers are currently seven points clear of the relegation zone with six games left to play.
However, with fixtures against Aston Villa, Manchester United and Everton in the final weeks of the season, Davies is eager for the Tigers to guide themselves away from danger sooner rather than later.
"I always thought we were in the mix, I've never felt like we were out of it," he told the Hull Daily Mail. "Our league form has to pick up because it's all good saying teams might not catch us but we have to do the job ourselves and make sure we're safe.
"You don't like to think too far ahead and only concentrate on your next game, but looking at the last week of the season we've got Aston Villa, Manchester United and Everton in the space of a week.
"We don't want it to come down to that. We want to try and be safe as soon as possible."
Hull's Premier League campaign continues on Saturday when they welcome Swansea City to the KC Stadium.