Paul Hartley's 21st-minute header put the visitors ahead before Roman Pavlyuchenko headed the equaliser three minutes before half-time.
"They really watered the pitch and made it slicker," he told BBC Radio Scotland. "We weren't allowed to practice on that.
"They put a bit of water on it this morning but nothing like that.
"So the speed of the game caught us out for the first 20 minutes.
"The players couldn't really even pass the ball to each other, they were sliding about and that wasn't what we practised on.
"You didn't have a clue what was going on. When we were practising the other day, the ball was holding up.
"It wasn't holding up tonight, it was going straight through."
Strachan hailed his side for adjusting to the pitch against the Russian league leaders.
"They are a right good side," he said. "They have won nine out of 12 matches on that pitch this season.
"They know how to play on it, they know every tweak, every spin, when the ball goes long, when it kicks up.
"So playing a good side on a very unusual pitch, to handle that was fantastic.
"This side tonight were better than Benfica last year, better than Copenhagen, that's for sure."