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Goals from Lewis Walker and Callum Stewart proved enough to see Harriers through at Aggborough, despite a second-half response from the visitors and a late save from Jack Wint.
Wotton was pleased with his side's defensive work but felt they could have made more of their opportunities in front of goal.
“I thought we were good for the vast majority of the game,” he said.
“We've worked so hard defensively in training, maybe we've neglected that attacking play a little bit.
“We could have put the game to bed first half and we had more than a couple of chances second half as well.
“I didn't feel uncomfortable second half, I thought we were defensively sound. Again, I'm a broken record, we can be better on the ball.
“But we're honest and we're hard-working. It's important we won today and in the FA Cup it's great. We can enjoy the draw.”
Walker opened the scoring after 15 minutes with his eighth goal of the campaign, before Stewart doubled the advantage eight minutes after the restart, turning David Davis's low cross beyond the goalkeeper.
Scott High reduced the deficit five minutes later, while Rhys Devine struck the crossbar on 72 minutes as Harriers looked to restore their two-goal cushion.
Wint then made a crucial save from Marvin Johnson's free-kick in the fourth minute of added time to preserve the victory.
“He had nothing to do again, but that's his focus and that's why he's going to be a top goalkeeper,” Wotton added of the Manchester City youngster.
“He's got a really, really good temperament. I've never seen a goalkeeper as focused as him before a game.
“He goes off into his own little world, really. We're grateful to have him.”
The victory came despite further injury concerns for Harriers, with Wotton admitting his squad is stretched ahead of a demanding run of National League fixtures.
“It's all hands to the pump at the moment,” he explained.
“The boys are honest, they're a fantastic group, they don't question it, they get on with it and they keep working.”
Wotton confirmed Connor Mahoney has suffered a thigh injury, while Callum Dolan was another concern following the tie.
He remains hopeful of welcoming players back before Worthing's visit next Saturday, while continuing to explore recruitment options carefully.
“It's imperative you don't just get bodies in for the sake of getting bodies in," he added.
“Every pound is important and I won't waste the owner's money. It's important that we get the right boys in.”
Worthing come to Aggborough for a 5:30pm kick off on Saturday with the FA Cup draw to be made on Monday night (19th).