Shields were beaten 2-1 at Hednesford Town on Saturday as they made it five defeats from seven games on the road this season.
They travel to Hyde United tonight sitting in seventh position in the Evo-Stik Premier Division table.
Joint manager Picton wants his team to put on a performance for the travelling fans. He said: “The supporters deserved more on Saturday.
“They deserve more than what we, as a group, are giving them in our away performances at the moment.
“It genuinely hurts Graham (Fenton), myself and all the staff, and I’m sure it hurts the players as well.
“We’re having some tough moments as a group, but we’ve got a great set of people in our dressing room and we just have to find the solutions to the challenges we face together.”
Hyde and South Shields were promoted together from the Evo-Stik North Division last season. Shields are nine places and eight points better off than their rivals but Picton admits that means little.
He added: “We’ve found out that every game is going to be a big test for us, especially away from home.
“There are a lot of players in our squad who need to respond in a really positive way tonight because if we’re not careful, the situation with the league table is going to get too far away from us and we’re going to be in a position that nobody wants to be in.
“It’s up to everyone in the camp to pull together, have honest discussions about how we move forward from here and put it right.
“Having this game just around the corner is probably a good thing after Saturday.
“There is no hiding place now. We’ve all got to show our mettle and show our determination and qualities across the board to put things right and get back to winning ways.”
Shields go into tonight’s game (7.45pm) without long-term injured duo Barrie Smith and Anthony Callaghan, but could welcome back captain Jon Shaw.