Noises that sounded like monkey chanting were heard during the game and Toure appeared to complain at one point to referee Ovidiu Hategan.
City spoke to UEFA's match delegate after the match at the Arena Khimki and intend to follow up by making an official written complaint after they return to Manchester.
Midfielder Toure spoke of his sadness over the matter at the end of the game.
The Ivory Coast international told Sky Sports: "It is quite disappointing when you're talking about people continuing to do that.
"It is unbelievable and very sad on my part.
"I think UEFA need to do something strong. It would be nice if we could stop that.
"Some of the songs today were quite stupid and I think UEFA has to do the work.
"Every time we say something it continues, something has to be done to stop it."
City went on to win the Group D game 2-1 after two goals from Sergio Aguero.
The incident comes 18 months after Porto were fined £16,700 by UEFA after their fans racially abused Mario Balotelli during a Europa League clash against City in February 2012.
City also lodged an official complaint on that occasion, when monkey-chanting had been prolonged and widespread.
Controversially, City were later fined £24,740 for delaying the kick-off of the second half of that same game by one minute.