Cole is unavailable after suffering a knee ligament injury in training on Thursday, a day after playing 45 minutes for England.
Cole has been understudy to Cesar Azpilicueta at left-back this season and faces eight to 10 days out.
"It was good for me that Ashley played a part of the game," Mourinho added.
"Unfortunately he got an injury in training and he's one of the players that is out. Lateral (knee) ligament, a little thing, but impossible for tomorrow and we would say between eight to 10 days."
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