United forced a 1-1 draw with the reigning European champions at Old Trafford of the Champions League quarter-final first leg on Tuesday but Bayern will have goalscorer Schweinsteiger missing after he was sent off.
Martinez will also be missing after for accumulating bookings and England winger Young said United will be going to Munich believing they can win.
Young said: "I can't wait to go to Munich. We have given ourselves a massive chance.
"I think everyone would have taken that result before a ball was kicked. It sets us up nicely for the second leg.
"It was a great team performance and we look forward to the second leg now.
"Everybody wrote us off before the game but we created many chances. We know they are a good team but we knew we would get chances on the counter attack. We managed to do that and got the goal.
"Schweinsteiger is going to be a miss for them. Martinez will be as well. But we have to concentrate on ourselves and put on a performance."
David Moyes' men had just 26 per cent possession, an all-time low for the club in the Champions League, yet enjoyed the better chances.
Midfielder Michael Carrick admitted it could have been even better for United if Danny Welbeck had not squandered a golden chance by trying to chip Manuel Neuer when one-on-one with the Bayern keeper.
Carrick said: "That is the one that sticks out. It would have been great if it had gone in but as it happened we managed to go 1-0 up anyway. Who knows what would have happened. It was a chance he would normally take.
"We are not getting carried away. The task ahead of us is tough. We will have to be right at our best to get the right result. But we still have a chance. We still believe we have a chance. We can go over there really positive."
Moyes will have Patrice Evra back for suspension for the second leg in Munich but the French full-back's stand-in Alex Buttner performed well against Arjen Robben and said he is determined to take his chance.
Buttner said: "I enjoyed the challenge. This is the biggest game to show myself. We have played against one of the best teams in the world and we have not given much away. Just one goal.
"We did well to stop Ribery and Robben and it was my chance to show I am ready. This is my chance and I have to take it.
"But Patrice helped me a lot, I appreciate that. Before the game he came to me and he wanted me to do well. That was nice afterwards he told me I played well. That is a good feeling."