Considine was carried off on a stretcher after hurting his knee when his studs appeared to get stuck in the soft pitch in Baku as he was barged at an aerial ball.
The 34-year-old lay motionless before going off after a long spell of treatment in the first leg of the Europa Conference League play-off.
Dons chairman Dave Cormack had criticised UEFA on the eve of the first leg for approving the use of the Tofiq Bahramov Republican Stadium and his reasons were soon evident.
Big chunks of turf bounced up whenever a player broke stride, the ball bobbled around, and the unstable surface seemed to play a part in Considine's misfortune.
Quoted on Aberdeen's official website, Glass said: "I said before the game I didn't want to use the pitch as an excuse. I deliberately didn't want to talk about it at that point and I didn't want to detract from the fact that Qarabag are a good team as we saw tonight and will probably see again next Thursday.
"But we've seen the reality of it there, it was a disgrace, and it probably resulted in Andy getting injured, which is a terrible thing to see happen at this level.
"The game shouldn't be played on a pitch like that, both teams deserve better.
"It was a game between two good teams, with good footballers on both sides, and they weren't given the surface to show their best."
The Dons struggled in the first half and fell behind to Jaime Romero's 30th-minute strike.
But they improved after Connor McLennan replaced Jay Emmanuel-Thomas at half-time and Christian Ramirez might have done better with a late chance.
"It was a tough game, as we knew it would be," Glass said. "The performance level, the fight we showed was brilliant especially second half.
"Bringing Connor on at half-time gave us chance to be a bit more aggressive, carry more of a threat in behind. We looked more compact and dangerous after the break, so the change served its purpose.
"We took the game to them a bit more, a bit more aggressive and playing higher up the pitch, and almost got our rewards for it. I think a narrow defeat is probably reward enough because we were under pressure a bit in the first half.
"We watched Qarabag on video before the game but you can't feel the heat when you're watching on your laptop or on the TV. It's a tough environment, the players aren't used to playing in that heat. That was tough, it saps the energy, but the players kept going.
"I've said to the boys that I think an average team gets beaten 3-0 or 4-0 here, but the heart and desire they showed and the ability to still carry a threat late in the second half, that was great character."