The Minstermen face Northampton Town at Sixfields on Saturday in a game that has huge ramifications at both ends of the League Two table.
While the Cobblers are aiming to keep their promotion quest on track, York know that they have three games left to save their Football League status.
"There is no room for fear and no room for nerves," said former Northern Ireland boss Worthington.
"It's about players giving big performances under pressure. Nerves have to be put to one side."
The appointment of the ex-Norwich City manager has sparked an upturn in fortunes at Bootham Crescent and he added: "The signs are good. The players have performed well in the last three or four games and I'm expecting them to continue."