England winger Johnson, 27, was arrested by Durham Police in the early hours of Monday morning for allegedly being involved sexually with a 15-year old girl.
Johnson has since been bailed as the investigation continues and Poyet, who was forced to suspend the player, admitted to feeling poorly about the situation.
"The only thing I can tell you is that it was a very difficult day yesterday," he said.
"Very difficult day. I've never had one like that, very difficult."
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