That precious point was gifted by Bath replacement fly-half Sam Vesty, who was ambushed by Tom Varndell while prematurely celebrating what would have been Bath's fourth try two minutes from time.
It leaves Newcastle with a much more difficult task when the Aviva Premiership's two bottom teams meet at Adams Park on May 5.
The visitors will need a sizeable win while denying Wasps a bonus point.
"We just have to win. It's in our hands," said Young of the game against the Falcons.
"Basically, if Newcastle come and win by that margin they deserve to stay up. Let's be honest about it.
"If we don't win our own game and the other team win by 24 points, we have to look at ourselves really."
Wasps led 9-0 at half-time and looked more than capable of winning at Bath, which would have ended the argument there but Bath rediscovered their form with three second-half tries.
"First half we kept it simple," said Young.
"We were in control and we needed a very strong second half, especially the first 20 [minutes].
"We talked at half-time about not becoming ragged or loose.
"Bath have got a lot of strike runners and if you give them space and loose ball, they are going to cause you problems. That's exactly what happened.
"We gave them a chance to get their tails up. They're a quality team - everyone knows that.
"I'm disappointed with our first 20 minutes in the second half which caused us all sorts of problems and got Bath back in front.
"But in the end we have to say we were quite lucky to come away with a losing bonus point."
Bath's outgoing director of rugby, Sir Ian McGeechan, makes no secret of the fact that he wants Wasps to stay in the Premiership.
"It's going to be one hell of a game in two weeks. I hope Wasps win," he said, acknowledging that Vesty was extremely embarrassed by his role in setting up a heartstopping showdown.
"Sam's been apologising ever since," said McGeechan, aware that the error had all but extinguished Bath's hopes of Heineken Cup qualification in a decidedly mixed season.
McGeechan's spell at Bath ends in a fortnight because of that failure to stay with the European elite.
"Five points today would have been very good," he said.
"But we've got a lot of things right here - I know some people may not think that.
"Sometimes it's been the ball going the wrong side of a post which has cost us four wins."
After a poor first half, Bath cut loose after the break, scoring tries through Lee Mears, Stephen Donald and Nick Abendanon.
"We were just more accurate in the second half," McGeechan added.
"We carried with real venom, got into the phases, stayed accurate and then we were always a threat."
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