Goals from James Forrest and Scott Brown condemned Heckingbottom to his first defeat as Hibs manager, with the Hibees exiting the competition at the last-eight stage.
Heckingbottom had clocked up three wins in a row in first matches at the helm of Hibs, but he accepted that Celtic's gulf in quality shone through on Saturday night.
"I'm disappointed because we are out of the cup," said Heckingbottom, "but Celtic were the better team, although we had some real good moments and a strong performance for an hour.
"We didn't have enough quality to really hurt them, so if that's the case, when you fall behind it makes the game harder.
"We were good, but Celtic were better."