Sacked by Milan after a torrid first half of the 2013-14 campaign, Allegri was appointed Juve coach after Antonio Conte departed last month, having guided the club to three successive league crowns.
His first game in charge ended in an embarrassing 3-2 friendly defeat to fifth-tier Lucento and Juve looked on course for another reverse on Sunday until two late goals saw them emerge 3-2 victors over an A-League All Stars outfit.
Allegri admitted afterwards that his side were yet to reach their optimum level.
"We made a few too many mistakes on an individual level and not just in defence," he said.
"It was a good game and a decent workout for the side particularly after the hard work we've got through in the last few days.
"There's still room for improvement. We made a quite a few errors but that's normal at this stage of our pre-season preparations.
"It's also to be expected, as the lads had heavy legs from the tough fitness work we've been doing in these two days in Sydney.
"We are certainly a while off competitive match tempo, but we are working towards it."
