Aaron Finch's second one-day international century condemned England to yet another defeat on a increasingly miserable tour, after he combined in a record 163-run opening stand with Warner (65).
England believed, however, that they had removed the left-hander on 22 when he walked after wicketkeeper Jos Buttler claimed a low catch.The standing officials, though, opted to review it and when the replays were not clear-cut, televsion umpire Kumar Dharmasena recalled Warner, who had almost reached the boundary's edge.
Afterwards Cook was certain the wrong decision had been made. "It might be my English eyes on it but I thought it was a pretty clean catch," he said. "It hit his fingers and bounced up. I only saw it a couple of times on the big screen and I thought it was the wrong decision.
"Obviously David thought it had carried because he was quite happy to walk off. It is strange because a lot of those catches look a lot worse on TV than they do in real life. That one I didn't see it hit the ground. We have to respect the umpire's decision."
Asked if it was a key moment, Cook added: "I think they were on around 80 so they had made a good start. They still needed 200."
England perhaps provided too many errors of their own to pin defeat on that one moment.
Sloppy fielding, which most significantly saw Gary Ballance drop Finch on eight, and a painfully slow start in comparison to Australia stood out as obvious concerns.
Cook's own form is, however, top of his list of worries after he failed to last the opening over before edging behind off Clint McKay.
The 29-year-old had already survived a strong shout for lbw from the first delivery of the day, and his problems were put into context when his opposite opening rival Finch won the game with his 121 from 128 balls.
"I need to start scoring runs to help us start turning games around," he said. "I can't keep asking the lads to do it if you're not doing it. I need a little bit of luck to get me going, but the way I hit the ball in practice [this morning], I know it's only practice and it counts for b***** all, but it was as good as I have hit the ball all tour."
Cook conceded the fielding performances - which have marked England's decline this winter - were now too frequently costing his side.
The impressive Chris Jordan could have removed both Finch and Warner before they reached double figures, only for catches to go down.
"The couple of dropped chances when you are defending 270 against a good side . . . you need to take every chance you get," Cook admitted.