York, second from bottom, are level on points with the team immediately above them, Torquay, but only two adrift of the next three clubs at the foot of the table, and Worthington remains confident the Minstermen can escape an immediate return to the Blue Square Premier Division.
Their hopes were dealt a blow by relegation rivals Accrington's last-gasp equaliser at the weekend, but Worthington senses there is plenty of fight left in his players.
"We were disappointed with the result on Saturday, but the performance overall was very pleasing," he said.
"We created a lot of chances but we've got to be more ruthless in and around goal. We cannot continue to hit the goalkeeper or put shots wide of the goal. We've got to take our opportunities.
"But even after the disappointment of conceding the late goal at the weekend, the spirit in the camp is still very good.
"In training this week the boys have been very bright. Performance levels are improving.
"The criteria and the demands we've been putting on players, letting them know what their role is within the team, they are taking this on board.
"We have to take this into the last three games. It's all about performing when it matters and we'll give it everything we've got."