Sassuolo came from behind to beat Juventus at the Mapei Stadium, with Adzic settling a wild finish deep into stoppage time after goals from Sebastiano Esposito and Bowie either side of a Juventus fightback led by Edon Zhegrova's double.
Speaking after the match, Aquilani was full of praise for his young substitute's impact.
"He's a young player, he has very high potential and he's started this season well. He's begun a new path, he's giving us great results, and now he has to understand that he mustn't settle, because the road is still very long, but if he keeps going like this he can only keep improving," Aquilani said.
The Sassuolo coach admitted the manner of victory, with goals arriving so late, made for an emotional night.
"It was an exciting match because goals at the very end create real emotion. Today it went well for us, the other time it went badly. I'd focus on this result, we produced the performance we wanted, we showed courage, and I hope the win gives the boys the awareness to keep improving, because the potential is very high.
"Hopefully we can sleep, because we have another match in a few days against Monza, but today the satisfaction is enormous."
Aquilani singled out veteran midfielder Nemanja Matic for his influence on the squad's younger players.
"I'm lucky to have someone like Matic, a champion with a capital C, he's a champion in every sense and he's helping me, producing incredible performances like today, and helping the young players who need figures like him to guide their behaviour, both on and off the pitch."
Juventus boss Luciano Spalletti, meanwhile, took some encouragement from his side's reaction after twice falling behind, despite the manner of the late collapse.
"I take with me the reaction, the desire to win the match, even though we lost our balance several times, and in some ways we'd managed to turn the game around, but we weren't able to see through what we'd built," Spalletti said.
The Italian admitted his team had lost their shape while chasing a winning goal in the closing stages.
"It's clear that you need to maintain balance and control over what happens next. By overloading one situation, one search for a goal, we lost our balance elsewhere, but we'd created the chance to go and win the match."
Spalletti also praised Adzic, who spent two seasons at Juventus before his summer move.
"He has a lot of qualities, a lot of positive attributes, because he has stamina, technique, he strikes the ball like few others, he's a footballer with his own creativity. Tonight he came on in the second half, he needs to play with continuity. Adzic will have important opportunities in the future."