The Minstermen were left bemoaning their luck after conceding stoppage-time goals in each of the first two games.
A week ago, it meant two dropped points at Tranmere Rovers while on Tuesday a ‘91st-minute’ strike by Doncaster Rovers’ Harry Forrester meant York crashed out of the Capital One Cup at the first round stage.
In both games, York performed admirably and had they triumphed then Worthington believes Tranmere and Doncaster could have had few complaints.
He said: “The past week has been a bit cruel for the lads but that is sometimes how football can be. It is the nature of the game and you just have to live with it.
“But the performances have been very, very good. We definitely didn’t get what we deserved but that is just how it goes. The good thing from my point of view is that the quality, the endeavour and the energy were excellent.
“I couldn’t have asked for any more in that respect. What I would like now, though, is for us to be a little more ruthless. If we can be, we will be fine.”
Like York, Northampton –who knocked Wolverhampton Wanderers out of the Cup in midweek – enjoyed a storming end to last season as Chris Wilder led the club to safety against all the odds.
Worthington added: “Northampton have had a good start, getting a good result last Saturday (beating Mansfield Town 1-0 at Sixfields) and then an even better one in midweek.
“We are well aware of the task in hand.”