Worthington felt his side were worthy of all three points - but for an outstanding display from home goalkeeper Steve Mildenhall.
Mildenhall made two superb second-half saves to deny the struggling Minstermen a desperately-needed win at the Memorial Stadium.
He dived to his left to keep out a close-range shot from Chris Smith after 70 minutes, and five minutes from time the tall keeper arched his back to palm away a 25-yard drive from substitute Michael Coulson that looked destined for the top corner.
It meant the man-of-the-match award for Mildenhall, who had begun the game with an awful mistake that saw Josh Carson shoot wide with the Rovers keeper stranded after failing to collect a free-kick into the box.
Worthington said: "Now we have to maintain that for our last five games and if we do we will give ourselves the chance to get the results we need.
"Their goalkeeper has denied us. The save from Coulson was absolutely fantastic because it was a great strike and the ball was arrowing towards the top corner.
"Richard Cresswell did a really good job for us up front, showing all his experience, and there were other excellent individual efforts.
"We defended solidly and restricted Rovers to very few chances, which pleases me. I just think we could be more clinical in making our chances count."