Douglas Costa and Mario Mandzukic struck either side of half-time to earn the Derby della Mole bragging rights and set up a last-four meeting against Atalanta, who surprisingly knocked out Serie A leader Napoli on Wednesday (AEDT).
But although Juventus recorded a sixth successive home clean sheet, victory came at a cost for the Coppa Italia holders due to injuries sustained by Marchisio and Sturaro, who filled in at right-back.
"I replaced him not for the performance but for a blow to the knee from which he did not recover," Allegri said.
"He did good things and less good things but he has only played two full-back games and he had a good game.
"[Marchisio] had a good game, he had a knock on the adductor and I asked him to wait 10 minutes to let [Sami] Khedira enter.
"He made good movements in from the channel, making room for Douglas Costa."
With Napoli, Roma and Inter all eliminated, Juventus appear to have a relatively straightforward path to collecting its fourth successive Coppa Italia title, but Allegri is taking nothing for granted as he seeks yet more silverware in charge of the Bianconeri.
"Atalanta are a physical, technical, well-organised team," Allegri added of Juve's last-four opponents. "It will be a difficult semi-final, but we will be ready.
"I think Napoli are very focused on the league, the Coppa Italia has lost an important team.
"We have reached the semi-final for the fourth year in a row and I think it is a good result. All the boys have responded well. We risked a bit at the beginning of the match because we fell asleep. In the second half we had many chances and I'm happy.
"Our goals are clear, we must go on the pitch to always win the games. Torino had a good first half, but right now, playing against Juventus is not easy."