The Well scored in the opening minute through summer signing Henri Anier but eventually went down as Niall McGinna converted twice from the penalty with another goal from ex-Fir Park defender Mark Reynolds consigning the home side to a loss.
McCall said that having to return from Russia on Thursday night/Friday morning from their Europa League qualifier with Kuban Krasnodar was not an excuse for his players but it did contribute to the defeat.
"I don't want to make any excuse but I know what it was like (this time)last season against St Mirren (following a Europa League game at Levante) when we were hanging on with 20 minutes to go," McCall said.
"I thought, to get anything out the game, we needed to be going into the last 20 minutes ahead.
"It's only natural, you get back in your bed at seven o'clock in the morning after the flight. If you're still in there you can dog it out, but when you lose two goals like that, you could see the lift they got and we looked a bit leg-weary."
He added: "The better team won. You can't afford to gift teams goals, especially good teams like Aberdeen who have threats all over the park.
"Having said that, the third goal, if that's a penalty then there's six or seven penalties in a game.
"But that's not why we lost. We conceded two poor goals in quick succession."