The Tykes only avoided relegation on the final day of last season but get their 2009/10 campaign preparations up and running on Thursday when they face Buxton before hosting Hungarian side Ferencvaros on Saturday.
Davey told the club's official website: "We have to improve on last season and we know we should not have been in that position with the squad we had.
"Pre-season is crucial and we want to put a marker down early and go out and win matches. We started slowly last season and three or four points from those first five matches would have made a big difference.
"It is important to get into that winning mentality in pre-season and take that into the first games."