Australia's huge 381-run victory was tarnished by constant sledging between the players and in one instance finger pointing by Australia captain Michael Clarke to England fast bowler James Anderson. (Agencies)
Cook took exception at comments Australian opening batsman Warner had made the previous day at his media conference when he said England were frightened and singled out batsman Jonathan Trott.
"It does look like they've got scared eyes at the moment. The way that Trotty (Jonathan Trott) got out today was pretty poor and weak. Obviously there's a weakness there and we're on top of it at the moment," Warner told reporters.
Cook said Warner had been disrespectful in his comments.
"I think for any professional cricketer, really, yeah," the England skipper said.
"On the pitch it's pretty much a war, isn't it anyway? So there's always going to be a few words on the pitch. I think that's the way people want to watch cricket being played. Tough, hard cricket. On the pitch is fine."
Asked if the rival teams hated each other, Cook said: "I think when you play each other for quite a few games in a row, the niggles can increase. It's competitive cricket."
England and Australia are playing 10 Ashes Tests compressed into in seven months.
Counterpart Clarke said when asked if Australia have over-stepped the bounds of acceptability through their on-field actions: "Not that I've seen through my career.
"I think I've heard a lot worse said on a cricket field than what any of the Australian players or the England players have said throughout this Test match," he said.
Australia's huge 381-run victory was tarnished by constant sledging between the players and in one instance finger pointing by Australia captain Michael Clarke to England fast bowler James Anderson.