The Ivory Coast striker was absent from the matchday squad at Villa Park as second-half goals from Romelu Lukaku and Leon Osman gave Everton a 2-0 win.
And Martinez has confirmed that the forward's omission was due to a knock he suffered in training during the week, although the Spaniard does not expect Kone to be out for long.
"It (the knock) was during the last game against Hull City," Martinez told the club's official website.
"He received the ball and then got a strong challenge on his knee.
"We're hoping that it's not going to be too much of a serious problem, but he's going to miss the best part of four days."
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