A fifth-minute strike from Greece winger Charis Mavrias, his first goal for the club, was sufficient to overcome the non-league battlers, who acquitted themselves well against their Premier League opponents.
Having made 10 changes from the midweek League Cup semi-final win over Manchester United, Poyet acknowledged that it was far from straightforward against a spirited Kidderminster side.
However, he was pleased with a professional performance.
"It was probably expected, but then we needed to win," he said. "Of course, a new group of players playing together for the first time - I think they were very brave in the first 20 minutes, very, very good."
Poyet fielded two debutants in Argentinian defender Santiago Vergini - signed on loan until the end of the season from Uruguayan club Atletico Fenix - and goalkeeper Oscar Ustari - recruited having left Almeria - and Poyet expressed satisfaction at his makeshift side's display.
"We need to just concentrate on Oscar Ustari, Santiago (Vergini) at the back and a few players that haven’t been playing like (Modibo) Diakite or (Valentin) Roberge or Charis Mavrias – they got 90 minutes, which is great for them.
"That was most important, and of course being in the draw tomorrow."
The Uruguayan was also quick to turn his attention to his side's Premier League challenge, with two vital cup wins in a week providing a platform from which he hopes to build.
"If you asked me what is important for us now, it's just to win games and to feel that we can be strong at home," he added.
For Kidderminster, the result marked the end of their cup adventure which saw them come into the match as the lowest-ranked team still left in the competition.
Manager Andy Thorn expressed pride in his players' performance, and is hoping that it will prove to be a boost in their bid to win promotion from the Conference.
"I'm immensely proud of my players," he said. "I thought they were magnificent. We looked like a league club. If that's not a springboard for our season, then I'll be very disappointed."
"We knew it would be really tough playing a Premier League side and, when we conceded so early, you know you're in danger of ending up with a cricket score. But, for us to be disappointed with not coming away with a draw and getting another crack at them speaks volumes for the performance."
