Mikael Lustig fired in his first Hoops goal from a Paddy McCourt corner in the 11th minute, but a disastrous mix-up between the Swedish defender and keeper Fraser Forster in the 53rd minute allowed Tim Clancy to equalise.
Lustig helped force in a second via Hibs skipper James McPake after Easter Road keeper Ben Williams had made a mess of a Filip Twardzik free-kick, but again poor defending by the champions allowed Paul Cairney to slip all too easily into their box and level with a drive.
Afterwards the Celtic boss denied the result had taken the gloss off a great week in which his side won through to the Champions League group stages for the first time in four years to be drawn with Barcelona, Benfica and Spartak Moscow.
"Barring the two goals I was pretty pleased with the performance," he said. "We murdered them first-half but if you miss easy chances and if you give away the goals of the nature we gave away you are always fighting to win the game. But I am not angry, I am just a little bit annoyed.
"We missed simple chance after simple chance and we can count ourselves very unlucky not to win the game today. We should have been out of sight at half-time. On chances alone we could have won two games."