The Minstermen had limited chances throughout the game with Tom Allan going closest after seeing his header cleared off the line in the first half.
Worthington was pleased with his team's commitment and also hailed a first clean sheet in three games.
"The game was a real battle and neither team wanted to give much away," he said.
"It was a competitive game and I can't fault the team for their work rate and commitment. It was scrappy but you're not always going to get silky football in League Two.
"We were resilient when we had to be and I'm pleased with the player's commitment.
"We do need to be a bit more composed in the final third and we could do with playing an extra pass to open things up. Out of the three league games we've had so far that was the lowest amount of chances we've created.
"After conceding six goals in our past two games we had a look at our defence because if you're conceding goals then you've a chance of losing games. I brought Daniel Parslow into the team and it tightened things up and I'm pleased we got the clean sheet."