Allegri - who was sacked by Milan in January - was surprisingly appointed as Antonio Conte's successor in the close-season after the now-Italy boss led the Turin club to three successive Serie A titles.
However, the 47-year-old has made a strong start to life in the Juve hotseat, leading them to four wins from four competitive fixtures without conceding a single goal.
And speaking to Radio Anch'io lo Sport on Monday, Marotta praised the work done by Allegri so far.
"After what Conte did here the scepticism over Allegri was understandable," he said.
"When replacing a coach who has won three successive Scudetti and set so many records the backlash can be negative.
"This is because the coach is the leader of the group, but I believe also that behind the coach and the team there has to be a strong club with the right to support the role of the coach.
"We have to give great credit to Allegri - he did well at Milan and was not an unknown when he arrived.
"He won the Scudetto in his first year, he is a winner and when we gave him the squad we did it responsibly, knowing that he had the right attributes to coach Juventus."
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