The Ivory Coast were one of the pre-tournament favourites for the African showpiece that is being held in Equatorial Guinea.
However, the1992 champions started Group D with a disappointing 1-1 draw against Guinea, Seydou Doumbia's 72nd-minute equaliser sparing the Ivory Coast's blushes.
Coach Renard stated that he felt talismanic skipper Toure appeared jaded in that game and believes the team will struggle if the Manchester City midfielder does not up his performance level.
"I think Yaya was a bit tired at the end of the game so it was better for him to come off, but he is a big competitor so he'll be ready for the second game," Renard said ahead of the encounter with Mali in Malabo.
"He has a big responsibility now, with the captain's armband. I expect a better second game from him than the first one.
"If he is not able to improve his level it will be difficult for the team."
Renard will have to rejig his forward line after Gervinho was sent off against Guinea for lashing out at Naby Keita in the 58th minute.
The Roma man will now miss the last two group matches through suspension and Renard, while showing some sympathy for the former Arsenal forward's indiscretion, stated that Gervinho was in the wrong.
"I said to him that he shouldn't have done what he did, but I also said to him that I did the same thing when I played football," he added.
"It is the kind of thing that we shouldn't see on a football pitch but sometimes things happen on the pitch and you get a bit carried away by the pressure or the intimidation of the opposition."
Mali have lost their last four meetings with the Ivory Coast, including a 1-0 defeat in the 2012 Africa Cup of Nations semi-final.
However, Henryk Kasperczak's side proved they are no pushovers in Tuesday's 1-1 draw with Cameroon and were only denied victory by Ambroise Oyongo's 84th-minute leveller.
Mali's goalscorer in that game, Sambou Yatabare, was disappointed to settle for a point, but feels the team can take heart from the draw.
"We had a great game," he said. "We were strong defensively and I am sure we can take that going forward."
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