Since making a flying start to life under the new boss, the Red Devils have hit a serious slump.
Six defeats have been suffered across their last eight games in all competitions, with the latest of those seeing them humbled 4-0 by Everton at Goodison Park.
Things are not about to get any easier, with United’s next two games set to see them lock horns with title-chasing City and fellow top-four hopefuls Chelsea.
A derby outing at Old Trafford is next on the agenda, with Young vowing that collective standards will be raised in a meeting with old adversaries.
He told MUTV: “We've just got to apologise to the fans and we've got a tough one coming up on Wednesday with the Manchester derby.
“We know how important that's going to be. If you can't get yourselves up for the Manchester derby, there's something wrong.
“I've got confidence that we're going to be ready for Wednesday. It's a disappointing day [against Everton] but we've got to dust ourselves down fairly quickly and go again this week.”
Three of United’s remaining Premier League fixtures are due to be staged on home soil, offering them hope in an ongoing bid to secure Champions League qualification.
Their only trip out on the road is set to take them to already-relegated Huddersfield on May 5.
Young believes Solskjaer’s side can finish with a flourish, with 12 points being targeted from four games that have plenty riding on them.
The versatile 33-year-old added: “It's four games, it's four winnable games.
“If you'd said in October, we would be in this position we'd have taken it, but a club like Manchester United, we should be looking much further up the table.
“We've got four games left, we've got four wins to get. It's going be tough but I'm sure we can do it.
“We were 4-0 down and [the fans] were still singing. They've been fantastic and we've got to go and put a performance in on Wednesday.”