Tries from England captain Chris Robshaw, Ugo Monye, George Robson and Jordan Turner-Hall earned Quins a bonus-point victory and secured them a semi-final berth while heaping more misery on Wasps.
It emerged midweek that the Aviva Premiership strugglers could be facing administration next month while the build-up to the Quins clash saw relegation rivals Newcastle move to within four points of them with victory at Gloucester.
On the field Wasps put up a good fight with scores from Christian Wade and Ross Filipo while Nicky Robinson kicked seven points - but it was little consolation for Young.
"It doesn't get much tougher than this week," he said. "When people are starting to worry about whether they've got a job in four or five weeks' time - surely it doesn't get any tougher.
"It's my job to keep players focused, it's been going on obviously for a long period now - it's a standard question I get asked every week.
"Obviously it's a bit more serious than we all thought initially
"You have to put that to the back of your mind if you can, I'd be a liar to say that it's easy because it's not but we have to go out there and do a job for each other basically.
"Our side of the bargain is to make sure we've got Premiership rugby, we've got to do the best that we can because make no bones about it we're going to be a far more attractive team playing Premiership rugby.
"Harlequins are a quality team and we struggled to handle their tempo, their intensity, especially first half.
"We've got to dust ourselves off now and go down to Bath next week and obviously try and get that win down there."
For Quins, victory represented a huge turnaround in fortunes after their 37-8 Amlin Cup defeat at Toulon last Friday and boss Conor O'Shea was delighted to see them wrap up their Premiership play-off berth.
"For us, there were no demons from France," he said.
"I think Wasps showed against Biarritz, if you switch off, the pace they have with people like Christian Wade and Tom Varndell, they're going to hurt you and that's a good lesson for us to learn but we know we've got plenty more.
"Psychologically and mentally the job was done, changes were made and the guys came on tried to make an impact but the game had become a bit disjointed by that stage.
"Is next week (Premiership game against Leicester) the be all and end all? No it's not, but it'll be a great contest because I'd like to reflect for the second time in play-off history - we're now in it.
"That's one thing ticked we now want to get a home tie.
"There's a lot of rugby to play but I was happy with the ambition and the physicality of some of our play."
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