Celtic are flying high in the Scottish Premier League, leading champions Rangers by a point, and were expected to put the Norwegian side to bed but were outclassed at their own backyard.
A packed home crowd were silenced in the 6th minute when Runar Espejord opened the scores for the visitors, who added a second through Amahl Pellegrino ten minutes after the break.
Daizen Maeda pulled one back for the hosts in the 79th minute but Bodo/Glimt restored their two-goal cushion just two minutes later through Hugo Vetlesen.
"Obviously it's not the outcome we wanted and from our perspective, we weren't able to reach the levels we were hoping to," Postecoglou said, as per the club's website.
"We controlled the game for the most part, but obviously they got their goals and they were pretty clinical in the way they counter-attacked against us, and we lacked a little bit of quality in the front third ourselves, although we did have our chances, so we paid that price.
"It was disappointing because we got ourselves back into the game, and we were controlling the game at that time – I think they probably had two chances in the second half.
"The second one's deflected and gone in, but you've got to take those hits and from our perspective, it's about making sure we dust ourselves off and go again tomorrow.
"You could sit here and feel sorry for yourself, or realise that there's still another game to go, and we can turn it around. That's the reality of it."