New signing Liel Abada had put Celtic ahead late in the first half before Nir Bitton was sent off on the stroke of half-time for a second yellow card.
Midtjylland were also reduced 10 men when Anders Dreyer received a second booking in the 56th minute, but Brazilian forward Evander still levelled on 66 minutes.
“We deserved the three points, Postecoglou said. “We played really well, especially in the first half. We controlled the game, scored a good goal and hit the post.
“We went down to 10 men for a significant amount of time and had to work hard. We created some good chances again and limited them to two strikes on goal throughout the whole game so its a wee bit of a missed opportunity. At the same time, it was a fantastic effort from the players.”
He also praised new recruit Abada who has joined from Israeli club Maccabi Petah Tikva.
Liel was bright, intelligent with his movement, scored a good goal and created a couple of good chances so it was a very promising start,” he said.
Elsewhere in qualifying, Rapid Vienna won 2-1 over Sparta Prague, while Dinamo Zagreb triumphed 2-0 at home to Cypriot club Omonia Nicosia.
Romanian outfit CFR Cluj won 2-1 at Lincoln Red Imps, Hungarian club Ferencvaros triumphed 2-0 over Lithuanians Zalgiris and Moldovan side Sheriff won 1-0 at Alashkert.