The Minstermen are three points above the League Two relegation zone after Worthington's first game in charge ended in a 3-2 defeat at fellow strugglers AFC Wimbledon.
The 51-year-old manager was told there was scope for team strengthening by the Bootham Crescent board when he replaced Gary Mills last week and although he made Sheffield Wednesday goalkeeper Arron Jameson his first loan signing last week, Worthington is not sure the right players are available.
"We have a limited time and have got to go the right way about things," he said after the loss at Kingsmeadow.
"If there are players available to come in on loan I will look at that but, at this stage of the season, there are not many managers of other clubs looking to do business.
"You can perhaps get younger players, but this situation might not be for younger players."
York will be chasing their first win in 13 league games at Bootham Crescent against Rochdale on Tuesday night and Worthington said his early impressions were that his current squad were capable of steering clear of relegation.
"I'd like to think from what I have seen during my first week at the club and in the first game that there is enough in the dressing room to get the points we require," he added.