"We knew it could be a risk for him to play the two matches," Silva told a news conference on Thursday. "We communicated this to them but we cannot control their decisions.
"We advised them... that it was a risk to play him in two matches in a short period. They decided and unfortunately for us and for Yerry he took the injury."
Mina joined Everton from Barcelona in August and has been restricted to nine league starts for the Merseyside club due to a persistent foot injury.
"He's not out for the season," Silva added. "Let's see how many weeks it will be but I expect Mina... to be playing in a blue shirt again before the end of the season.
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"It hasn't been an easy season for him since he joined the club, he's had some unlucky moments and some bad injuries."
Everton, who are 11th in the table, visit ninth-placed West Ham United on Saturday.
(Reporting by Rohith Nair in Bengaluru, Editing by Simon Jennings)
