He apologised for his actions but the FA announced he had been charged with misconduct. Klopp has until 1800 GMT on Thursday to respond to the charge.
"I told him how much I respect his work.
"What can I say about it? I didn't want to run.It was not in my plan. I didn't want to run to Ali (goalkeeper Alisson), I couldn't stop obviously. Not cool, but it happened."
Silva said he did not hear an apology from the Liverpool boss, and added: "To be honest, I didn't see so I don't know what he did and how he did it."
The last-gasp win took unbeaten Liverpool to 36 points -- just two behind leaders Manchester City.
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