The Rossoneri scored two late goals through Cristian Zapata (deflection off Emilio Izaguirre) and Sulley Muntari to record maximum points against a Hoops outfit who did a fair amount of attacking at the San Siro.
De Jong admits Milan rode their luck throughout and was thrilled to come away with a vital victory in Europe's premier club competition.
"It was a lucky win but sometimes you need some luck to win games. We started off quite well but we let Celtic get back into it in the first-half," he said.
"We tried to play a little bit in the second half and then you see two lucky goals, that's football.
"Mentally-wise, they were a lot stronger today. You know that when Celtic come to play on your pitch, you have to play at 100 per cent."