The Minstermen are second from bottom in League Two and face a relegation dogfight over their remaining three fixtures that Worthington senses will go down to the last game of the season.
Worthington, who replaced Gary Mills as boss seven games ago, takes his side to promotion-chasing Northampton on Saturday before their final home game against Southend and a last-day clash at Dagenham & Redbridge.
"In the next three games there is no room for fear and no room for nerves," Worthington said.
"It's about players giving big performances under pressure. Nerves have to be put to one side.
"But the signs are good. The players have performed well in the last three or four games and I'm expecting them to continue."