Young was withdrawn at the interval on Sunday following a heavy collision with Daniel Agger while Vidic suffered a blow on the head during an aerial challenge inside the Merseysiders' box.
Meanwhile, Sir Alex also informed MUTV that both Wayne Rooney and Nani will feature in the FA Cup replay with West Ham on Wednesday although Jonny Evans is unlikely to be risked with the trip to Tottenham on the horizon.
Despite reports that Young left Old Trafford on crutches and skipper Vidic had a knee problem, Sir Alex is not overly concerned with their fitness - even if the winger looks set to miss the midweek tie and Sunday's clash at White Hart Lane.
"Actually, Vida's knee is okay," declared the boss in an exclusive interview with MUTV. "It was concussion. He had a little bit of concussion but he's okay and fine. He trained yesterday and was good.
"There are no other serious knocks really. I think they're all pretty good. Obviously, Young has got a dull knock, a little bit of a strain on the knee, but it's nothing serious. I think he'll be back next week. Maybe not for Tottenham but, the week after, he should be okay."
The full exclusive interview with Sir Alex will appear in MUTV's Matchday Live, this Wednesday at 16:00 and 19:00. To subscribe, visit manutd.com/joinmutv.