Young, who castigated his team after their 22-17 defeat at Cardiff Blues on November 9, was thrilled to see his players produce a positive response.
"If we had lost again today, we would have pretty much needed a miracle from the last two group games to go through," the director of rugby said.
"But it goes down to the last two games now and we are in with a shout.
"We played a very experienced Worcester team. It wasn't the perfect performance but I was really pleased with a lot of aspects."
Young had criticised his team for failing to show "the bite and hunger" he expects as they went down against Cardiff.
But he said: "We had a lot of bite in the way we played the game today. We brought a lot of quick ball and were aggressive.
"A lot of players showed me what I knew they could do. They have to go out and push their claims and last week a lot didn't.
"This week they stood up and showed they want to play for Wasps and put pressure on me when it comes to selection."
His young pack delivered a solid foundation for the backs to play off and Young had a special word of praise for 23-year-old lock Josh Thomas Brown, borrowed from Championship side London Scottish to fill in with Tom Palmer and Joe Launchbury on England duty and Marco Wentzel injured.
"He was excellent. He picked up everything very quickly in the week and did a great job for us," Young said.
Tommy Bell, the 20-year-old third-choice fly-half, contributed 13 points - with five kicks from five attempts - in the absence of injured Wales internationals Stephen Jones and Nicky Robinson.
Robinson could be fit for next Sunday's Aviva Premiership home clash against Leicester Tigers, with Jones a possible further week away, but neither will kick better than Bell did against Worcester.
"He's played a lot of positions over the last couple of seasons in his development but the one thing that has been consistent has been his goalkicking," said Young, who also expects England-capped scrum-half Joe Simpson "back in the mix" to face Leicester.
Nigel Redmond, Worcester's assistant head coach, blamed his side's defeat on "a lack of accuracy".
He said: "It was very frustrating but this is a competition for young players.
"It's a great opportunity for them to put pressure on the usual starting players and, as far as effort and endeavour go, they have made a step forward."
Praising the Warriors youngsters, he said: "Richard de Carpentier had a massive game in the back row, prop Ryan Furniss came on at half-time for Ceri Jones, Ben Howard came on and scored and Andy Short, who also scored, did really well.
"But when it came down to the kickers I thought Tommy Bell had a great game for them."
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