Young did admit to being "over the moon" at beating reigning champions Saracens and now their predecessors in the season's opening two games.
But after Sunday's 35-29 win, he also warned that in other circumstances they could easily have been bottom of the pile going into next weekend.
"You have to be realistic. Nobody goes into a game thinking anything other than why you can win. But you do feel good about winning games likes the ones we've won," Young said.
"You can be over the moon as long as you accept that both were also games we could have lost. I am aware of that and so are the squad. Last season's stats show that Wasps had the worst lineout and the worst scrum which is why they finished ninth.
"So we are a work in progress, working to improve."
Young singled out young wing Christian Wade for special praise after the former Wasps academy player scored a sizzling hat-trick of tries in only his sixth first-team game.
Young added: "Christian is a rare commodity in the game. Give him the ball and people shift to the edge of their seats in anticipation. Considering his age, that is very impressive.
"But he is very new to this level and we'll make sure he is brought along at a sensible pace."
Leicester rugby director Richard Cockerill remained upbeat despite a second defeat to start the season and hailed Billy Twelvetrees, who scored all Leicester's points with two tries, two conversions and five penalties.
Cockerill said: "It was a good game. I'm pleased with the lads because there's losing and then there's losing after playing well.
Had we been a bit smarter near the end, used lineouts to our advantage, we could have come away winners, but the lads put in a lot of good work.
"We are disappointed because we needed to be a bit more composed on the ball.
"They tell me this is the first time we have lost the first two games of a Premiership season, so I guess I'm setting records of some kind. But if we continue showing this work ethic the wins will come.
"We all know that Billy is a quality player and he did ever so well to step up at the end and kick that goal to make sure we went home with at least a point. We deserved the point, but were punished for making too many errors."
Wade also earned Cockerill's praise for his eye-catching display.
"Wade certainly has pace, and tries don't come much better than his second against us. I want England to pick him now, immediately, whisk him down to New Zealand - so we don't have to face him again."
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