The Red Devils held the defending champions at Old Trafford on Tuesday in the first leg of their quarter-final tie.
Young now believes that United are more than capable of progressing when they travel to Germany for the return leg next Wednesday.
"I can't wait to go to there. Everybody wrote us off before the game but we have given ourselves a massive chance," he is quoted as saying by Sky Sports News.
"I think everyone would have taken that result before a ball was kicked. It was a great team performance and we look forward to the second leg now - it sets us up nicely for that game."
United return to Premier League action on Saturday when they face Newcastle United at St James' Park.