Cook insisted a "line had been crossed" after Sachithra Senanayake ran out England's Jos Buttler as the non-striker backed up during Sri Lanka's 3-2 series-clinching six-wicket win in the fifth and final one-day international at Edgbaston on Tuesday.
Sri Lanka captain Angelo Mathews, asked by the umpires if he wanted to uphold what was a legitimate appeal, didn't call Buttler back and the wicketkeeper, whose blistering 121 had so nearly taken the hosts to victory in their seven run fourth ODI defeat at Lord's on Saturday, was out for 21.
"I was pretty disappointed with it to be honest with you. You don't know what you'd do if you were put in that situation, the heat of the moment, until you are. I'd hope I wouldn't do it."
But Sri Lanka captain Angelo Mathews insisted Buttler had been repeatedly warned before Senanayake took the bails off to send Buttler on his way.
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This was only the eighth reported instance of a batsman being run out backing up in an international match and the first since South Africa's Peter Kirsten was dismissed by India's Kapil Dev in a one-day international at Port Elizabeth in 1992/93.
"This is just different," said Cook. "For some reason it's different. In my opinion there's a line and that line probably, I think, was crossed today (Tuesday)."
"If he (Buttler) was properly trying to steal a single, I could possibly understand it.