The Minstermen, unbeaten in their last fives games, winning three of those, climbed two points clear of the relegation zone by beating Southend 2-1 in their final home game on Saturday in front of their biggest crowd of the season, 5,975.
"I've been amazed by York City's supporters since day one when we were playing at Wimbledon and 500 were in the away end," Worthington told the York Press.
"The support home and away is phenomenal and we just want to give them something to smile and shout about."
York travel to Dagenham & Redbridge in their final game on Saturday without having to rely on other results to ensure another season in League Two.
"We've got one game left and it's in our hands," Worthington added.
"We're in a good position because we know what we need to do and are only focused on that game now."