Fresh from winning through to their first Champions League semi-final in 12 years after beating Monaco in midweek, Juve took their eye off the ball domestically and suffered a second defeat in three Serie A matches.
"All we had to do is be patient," Allegri said after Juve's first derby loss in 20 years.
"We were ahead, why would we run after that second goal? They had to open up and go for it. We had to force our nature when we shouldn't have.
"We didn't lose because of defensive mistakes. We lost because of the match management."
Andrea Pirlo put the visitors in front at the Stadio Olimpico with a trademark free-kick that went in off the bar 10 minutes before half-time, but Torino produced a tremendous fightback to claim a first win in the city derby
Fabio Quagliarella was the hero for the Granata against the club he left last summer as he set up Matteo Darmian to equalise just before half-time and then netted what proved to be the winner from close range 12 minutes into the second half.
In any case, even a win for Juve would not have been enough to clinch the title with six games to spare as second-placed Lazio drew 1-1 with Chievo at the Stadio Olimpico in Rome.
The veteran Miroslav Klose put Lazio ahead on the stroke of half-time only for Alberto Paloschi to volley the visitors level with quarter of an hour remaining in the capital.
Lazio are 14 points behind Juventus in second place, and a win at home to bottom club Parma on Wednesday will force the leaders to wait even longer before wrapping up the scudetto.
However, if they slip up at all, Juventus will secure the title with a win at home to Fiorentina.
Lazio are a point clear of rivals Roma in the chase for Champions League qualification after Rudi Garcia's men continued their poor second half to the season by losing 2-1 to Inter at the San Siro on Tuesday.
Europa League semi-finalists Napoli closed the gap on Roma in third to just two points with a convincing 4-2 home win over Sampdoria, who are fifth, later on Sunday.
Elsewhere, Parma earned themselves a reprieve from relegation for now after Antonio Nocerino's first-half penalty secured a 1-0 win at home to Palermo.
Genoa remain in the running for a Europa League place after defeating relegation-threatened Cesena 3-1 while Luca Toni scored twice in Verona's 3-2 win at home to Sassuolo and German Denis netted in stoppage time to secure a 2-2 draw for Atalanta at home to Empoli.