Goals from Ollie Pearce (2) and Callum Kealy helped the Mackerel Men book a trip to old foes Bognor Regis Town in the quarter-finals.
Worthing had been inconsistent in their last three outings - recording a draw, a win, and a loss - but Hinshelwood said Saturday’s win was a return to form.
He said: “I thought it was a really good performance. They’re a really good side.
“A lot has been made about the amount of goals they score, but I thought it was a really good defensive display. But perhaps we should’ve taken more chances going the other way.
“All in all, we looked solid at the back and creating chances the other way. It’s a far cry from what it has been.
“I thought they applied themselves brilliantly. We defended the box with a lot more aggression and got into good areas, and at the same time we looked a threat going the other way.”
Pearce’s penalty opened the scoring for the Mackerel Men on 22 minutes after Joel Colbran was felled in the area.
Kealy then doubled Worthing’s advantage on 35 minutes, sweeping home from Reece Meekums’ excellent cross.
Pearce sealed the win on 67 minutes. Worthing’s top goalscorer blasted in off the post to secure the Mackerel Men’s place in the final eight.
Worthing visit fierce rivals Bognor Regis Town on Monday, December 27 for a hotly-anticipated West Sussex derby.
And Hinselwood said that the Mackerel Men’s convincing Senior Cup win, coupled with a full week of training, will put his side in good stead for their derby day clash.
He added: “It will be good to get the players in for a full week’s training so we’re ready to go for Monday next week.
“There were some real journeys we had to go on last week. Haringey, Brightlingsea and Margate all in a week is tough.
“Off the back of that [win against Lewes], hopefully we’ll go into games in the Christmas and New Year period with a lot of confidence.”