FCM won 3-2 at the City Ground with former Bournemouth midfielder Billing outstanding on the night.
He said at the final whistle: "We knew it was going to be a tough game, so we're delighted with the result. We had to work our socks off; they are top players, a top team. The crowd was with them as well, so we just had to work hard, and it paid off.
"Today was a test for us. We knew we're strong in the Danish Superliga, but we were competing against a top Premier League side, and now we can see where we are as a team. Now we have to continue; we can't take our foot off the gas."
Teammate Mads Bech also said: "It was lovely! Just what we hoped for - a lot of happy faces in the dressing room after the game. It was a team effort; everyone was working as hard as we could, especially second half, when we were under pressure. It took a team effort to get the three points, and we couldn't wish for a better start."