The Light Blues got their Championship campaign off to the worst possible start as title rivals Hearts beat them 2-1 thanks to goals from Danny Wilson and Osman Sow.
The second-tier curtain-raiser was played just hours after former Gers chief executive Charles Green announced he could be on his way back to the club as he claimed he was behind a multi-million pound investment bid.
McCoist said: "Whether he (Green) comes back or not, we don't know. It remains to be seen.
"But I thought the timing of it, again, wasn't great. It was a big day for the players and supporters, an even bigger day for Sandy Jardine's family. For the first time, one or two of the players actually mentioned to me about the timing of it and all that kind of stuff.
"Everyone does their level best to keep players sheltered and we will continue to do that.
"Because the only thing they can have a bearing on is results on the park and that's what they have to concentrate on. But sometimes it is just a little bit of a sideshow we can do without."
Whether Green comes back to Rangers or not, McCoist has plenty of work to do with his squad to get them in shape for a shot at the Championship crown.
A succession of missed chances proved costly when Wilson headed home and, even though Nicky Law netted in stoppage time, Rangers couldn't hold on as Sow sealed the victory.
The winner came just seconds after Darren McGregor replaced Richard Foster at right-back, with the former St Mirren star caught out of position as Robbie Neilson's side cut through the Rangers rearguard.
McCoist said: "Hearts saw a gap because Richard Foster had to come off injured. Darren McGregor went on and wasn't in his position quickly enough.
"I'll need to look at it again, because I'm not sure he was actually on the park quick enough for Hearts to take centre.
"But if not, we should have stopped the game and not let them take centre until we had regrouped into our positions. Darren definitely wasn't in position when they took centre.
"I'm not saying for a minute that's his fault, because he was just going on with Foster coming off struggling. I also thought there might have been a foul on Lee Wallace for the first goal, I thought it was a shove on his back before the corner. That would be a bigger gripe."