The win means that Milan just need a draw against Ajax in a fortnight's time in order to reach the second round, and De Jong said that he was delighted with his side's sharpness on the night.
"I was expecting a little bit more from Celtic, but we put them under pressure and took the chances when they came along," he told UEFA.com. "For Milan, the Champions League is as important as the championship. We are not in a good place at the moment, but three points and 3-0 is very welcome.
"We showed tonight how dangerous we can be. We were very sharp right from the start. We were lucky at the start of the second half with the chance Virgil van Dijk had, but after that we picked up the pieces and were comfortable. The next game against Ajax is now very important and we look forward to it."
Milan are second in Group H, one point ahead of Ajax and two behind Barcelona.