Samuel Mbangula and Timothy Weah struck Juve's goals in the second-half.
“We work every day to win, every moment of the day is hard work to put in the performance we did today and win,” Motta told DAZN.
“You win matches like this not just on the day, but all the time building up to it. I thank the lads who are working so hard, with great effort, overcoming the many difficulties we’ve had until now and this victory compensates them for all that.
“In the most recent match against Atalanta, we made some technical errors that gave our opponents confidence, whereas today we made fewer mistakes and psychologically that also made it clear to Milan that they were facing a team with intensity and quality.
“We wanted to be very aggressive, not allow Milan time on the ball and especially their goalkeeper who often is able to find teammates with passes. The lads showed great energy and it went well.”