The Russian side have lost their last three games and travel to Glasgow on Wednesday when a result for Celtic could see them progress to the last 16 of the Champions League.
McGeady swapped Scotland for Russia two years ago and believes his side can end Celtic's qualification dreams.
"Everyone is upset at recent results but we intend ending our bad run, starting this week," he said.
"We were all very disappointed losing 4-2 at home to Zenit at the weekend but personally I was delighted to be back playing after a spell out injured.
"We created enough chances to win the game but we didn't defend well enough against a very good team.
"Our main hope now for the rest of the season is that the fans don't desert us as we need them more than ever.
"I understand our fans are not in the best of moods right now but I would ask them to rally round the team at this difficult time."