The Tykes have won only one of their last five league matches and slumped into the bottom three following their home defeat to relegation rivals Blackpool over the weekend.
Davey said: "There were a few words said in the dressing room after the Blackpool game and we have to put it right. Everybody at this club wants to stay in this division and we have to make sure we do that.
"We need people to stick with us. I know there were a lot of disappointed people after the game on Saturday, but none more than me. With our fans behind us we will win matches, but we have to spark them.
"We have to give them a lift. We need them out in their numbers on Tuesday night, get behind the players and make sure they rally us on to a win."