The Minstermen were beaten by a goal in each half from Gareth Evans and Jamille Matt but Worthington believed both efforts should have been prevented.
Only fellow strugglers Cheltenham and Torquay United have now conceded more League Two goals than York this season and the Bootham Crescent club have also let in seven during two cup ties this term and 10 during their last four fixtures in all competitions.
On Saturday, the visitors found the net despite home goalkeeper Michael Ingham saving initial attempts with Matt’s second-half strike also following a carelessly-conceded free-kick by on-loan right-back Luke O’Neill.
Commenting on his team’s efforts to keep promotion hopefuls Fleetwood at bay, Worthington said: “We could have dealt better with both goals. They were both parried by the ’keeper and their players, especially with the second one, were intent on trying to score. We have got to be just as determined to clear the ball in those situations.”
Evans opened the scoring on 23 minutes, nodding home after Ingham could only push out Matt’s header from Steven Schumacher’s left-wing cross.
The visitors continued to look the stronger side after the break with Ingham saving from Evans (twice) and Jeff Hughes before his team fell further behind.
No one connected with Schumacher’s inswinging free-kick and Ingham could only palm it out as far as Matt, who finished emphatically into the roof of the net from six yards.
After Wes Fletcher had fired wide for the Minstermen and fellow substitute Ryan Bowman forced a rare save from visiting goalkeeper Scott Davies, Matt was then denied a blatant penalty in stoppage time when he appeared to be brought down by home captain Dan Parslow.
York City: Ingham; Oyebanjo (Fletcher, 46), McGurk (Allan, 38), Parslow, Davies; Montrose; Carson, O’Neill, Whitehouse, Brobbel; Jarvis (Bowman, 68). Unused substitutes: Kettings, Cresswell, Platt, Puri.
Fleetwood Town: Davies, Hogan (McLaughlin, 78), Pond, Cresswell, Taylor; Hughes, Schumacher (Brown, 86), Sarcevic (Blair, 90), Evans; Matt. Unused substitutes: Roberts, Parkin, Brown, Ball, Lucas.
Referee: K Wright (Peterborough).
Man of the match: Michael Ingham.