"It means a lot," he told MUTV. "It's the pinnacle of European football and to play that many games is obviously special."
However, Riggs was disappointed with the 1-1 draw at the Donbass Arena as United failed to hold onto an early lead and conceded the equaliser 14 minutes from time.
"When you're playing for United and you go 1-0 ahead, you expect to be able to see the game out," said the 39-year-old. "But fair play to Shakhtar - they've got some decent players and they put us under a lot of pressure. We've won our first game and drew a very tough away game so we'll take that.
"We are in a good position; it's a tough place to come this. Hopefully we can get a few victories from the next couple of games and that'll put us in a good position."
United are now second in Group A with four points from two matches.