Jake Cooper's volley put Millwall 2-1 up at the break after Michael Obafemi and Yakou Meite traded goals during an entertaining first half in South London.
However, Neil Harris' side controlled the second half, limiting the Bluebirds to scraps, before Duncan Watmore made sure of things in stoppage time with a cool finish.
The result lifts Millwall into 16th, six points clear of the relegation zone, while Cardiff are now 11th with three games left.
Bulut insists his side need to show a winning mentality in their remaining games this season.
"Millwall at home are a good team, they are fighting. I was satisfied with (C the first half, but with the second half, I have no words for the second half," he said.
"Nobody can tell me 'two days before we had a game and we were tired', Millwall also played a few days ago.
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