Worcester edged the match 20-19, but they should have been celebrating a far more comfortable victory after dominating much of the contest in terms of territory and possession.
Arscott was the home side's hero with both of their tries, one of which was a brilliant solo effort, and Davies heaped praise on the 24-year-old.
"Tom was excellent today, he was very assured at the back and his second try was something special," said Davies, who felt his side could have made more of their dominance.
"We are pleased to win but we could have been more clinical. In the first half we had 66% of possession but we turned off a bit in the second half," he said.
Worcester now face Bath next week in the same competition, and Davies is not expecting that to be an easy match.
"Every game in each competition is equally important for the club. We know we can do better and Bath will be a tough test," he said.
The two sides could not be separated in the opening 14 minutes today, but Worcester then stormed into a 10-0 lead in the space of four minutes, with Joe Carlisle slotting over a penalty before the fly-half converted Arscott's opening try.
Wasps hit back with a brace of penalties from Ryan Davis and Elliot Daly before half-time, and the visitors then took the lead when Daly crossed for an unconverted try in the 48th minute.
However, Arscott's second try, with the extra points added by Carlisle, put Worcester back in front at 17-11 - and they would never surrender that advantage.
Davis reduced the deficit with another penalty but then Carlisle slotted over a kick of his own to restore the six-point lead at 20-14.
Alex Cheeseman's 70th-minute try brought Wasps back to within one point, but the visitors were unable to convert that and Worcester held on over the closing stages to claim the win.
Wasps director of rugby Dai Young said following his side's defeat: "Our selection today was forced upon us, as in the last few games we have had injury after injury and we are very grateful that some clubs loaned us players today."
Young accepted his side were second-best in the first half but felt they had the chances to snatch the victory as the game wore on.
"We didn't have the ball in attacking areas in the first 25 minutes, they had all the possession but eventually we played with more belief and could have won the game for in the second half we scored some really nice tries," he said.
Wasps now face Newport Gwent Dragons at home next Saturday evening, with Young keeping his fingers crossed that some of his absent players will be able to return.
"Hopefully Joe Simpson will be back in contention and Dom Waldouck might be back from injury to play some part. We want to make Adams Park a bit of a fortress and will probably pick the best available side."
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