The Warriors overturned an interval deficit to win Saturday's LV= Cup opener at Sixways.
Scarlets were the better team in the first half and would have had a much greater lead than 13-6 had outside-half Owen Williams not missed three routine penalties at a crucial stage in the game.
Worcester then introduced Andy Goode and Ben Howard at half-time to replace out-of-sorts duo Nikki Walker and Jon Clarke.
And the changes paid dividends with Howard, Semisi Taulava, Jake Abbott and Neil Best all crossing for tries and Joe Carlisle kicking 14 points in total.
Redman said: "Both sides struggled to get any flow to their game in the first half. We had the intent there but the execution wasn't what it should be.
"We were far more physical in the breakdown area in the second half and passed the ball more.
"Because of long-term injuries to Walker and Clarke it was always the intention to give them only 40 minutes of rugby; we have to look after them long term.
"But Andy Goode gave us more life to our game. He and Joe Carlisle combined well with each other at 10 and 12."
Scarlets coach Simon Easterby admitted it was a game of two halves for his team, although he felt there was plenty to build on.
"There were lots of positives to take from the first half," he said.
"Our physicality was very good for a team that was thrown together during the week.
"In the second half they brought on some big ball carriers and we slipped off a couple of tackles.
"We only had 33 per cent possession and territory in that second half and two of their tries came off our mistakes, but we'll be better for the experience."
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