United drew 1-1 with the reigning European champions at Old Trafford on Tuesday, when Schweinsteiger, the Bayern goalscorer, was sent off. Martinez will also miss the second leg because of accumulated bookings.
Young said: "We have given ourselves a massive chance. Everybody wrote us off before the game but we created many chances. 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 put on a performance."
David Moyes' men had just 26% of the possession, an all-time low for the club in the Champions League, yet enjoyed the better chances.
The United midfielder Michael Carrick admitted it could have been even better for his side had Danny Welbeck not squandered a golden chance by trying to chip Manuel Neuer when one-on-one with the Bayern goalkeeper.
Carrick said: "That is the one that sticks out. It would have been great if it had gone in."
Moyes will have Patrice Evra back from suspension for the second leg but stand-in Alex Buttner performed well against Arjen Robben and is determined to take his chance.
The full-back said: "We did well to stop Ribery and Robben. This is my chance and I have to take it."