Juventus now top Group H after winning their first two games in the Champions League group stages.
"We have to go into the game looking to start on more of the front foot, especially at home", Young said.
Juventus are sweating over the fitness and availability of Emre Can ahead of Tuesday's clash with Manchester United after the summer signing was diagnosed with a thyroid problem that could require surgery.
"I think it'll be a good lesson for us, as this is a wake-up call, so everyone can remember that nothing is to be taken for granted".
The home side did push for more goals in the final 10 minutes of the first half, but Genoa defended well enough to keep the score at 1-0 at the break.
But Juve were made to pay for failing to convert a hatful of chances when Daniel Bessa headed in a second-half equaliser.
Higuain also scored 55 goals in 105 appearances in all competitions.
"It is disappointing, but we have to take the positives from the game and kick on from here".
"Like I say, on another day we could have gone on to get another goal, but it wasn't meant to be".
Ashley Young certainly has a point as Manchester United looked much more risky in the second half and were adequately rewarded in the form of two goals. He continued saying that he knew something had broken and then suddenly, the signing of Cristiano Ronaldo from Real Madrid was announced.