The two-time Heineken Cup winners' 32-15 defeat at Northampton means they are still just eight points above bottom club Newcastle with just four games left.
The clubs meet in the final game of the season at Wasps' ground and, while Young thinks there will be more twists and turns before then, he thinks Wasps will stay in the Aviva Premiership
He said: "We may as well chuck in the towel now if I'm not confident. It's going to be difficult, there are some good teams in this league.
"It's not going to get any easier for us, but it's in our hands.
"If we win games, they can't catch us, it's up to us to win games. If they win games and catch us fair play to them.
"I'd be lying if I said I had not got half an eye on them. We have got a bit of a cushion at the minute but it will evapoate very quickly if we don't get another win, maybe two wins.
"Newcastle will win games, we just have to make sure we get some points on the board to maintain that cushion."
Northampton scored four tries to earn a bonus point, England full-back Ben Foden scoring twice and the others coming from centre James Downey and substitute scrum-half Martin Roberts.
The other points came from the boots of fly-halves Ryan Lamb and Stephen Myler, while fly-half Nicky Robinson kicked five penalties for Wasps.
"We showed a lot of determination," Young added.
"But it wasn't quite good enough. We played against a very good Northampton team. It's very difficult to come here and get anything but the frustrating thing for me is we have to work so hard to get any points.
"We really have to scrap and then we let in some silly points like the last try from a scrum.
"That is pretty poor from our defence, we have to be better than that. We are contributing to our own downfall, but we were under pressure for big parts of that game and the players really stood up."
Young said flanker Jonathan Poff would be fit for next week despite breaking his nose, but that centre Dominic Waldouck was doubtful after injuring a hamstring strain.
Northampton jumped into third place above Leicester, who play London Irish on Sunday, and director of rugby Jim Malinder was pleased to get a bonus-point win after last week's defeat by Leicester in the LV=Cup final.
He said: "You always want to win the game first and then look for the bonus point. It took a long time to come but we got there in the end so we are pleased.
"We were not 100 per cent accurate, we were a bit rusty in a few areas, but you have to give credit to Wasps, they never give up."
Mallinder admitted it had been an interesting week after the cup defeat and with disciplinary hearings looming next week for Dylan Hartley and Calum Clark, who was suspended by the club for the Wasps game after an incident against Leicester left Rob Hawkins with a broken elbow.
He would have liked to have had Hartley's hearing to have been this week, adding: "You want to get on with it. It's disappointing that Dylan has come here under a cloud, but that is where we are."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.