NEXT time put on a pair of pants!” That’s what “Die Hard” star BRUCE WILLIS told his rebellious daughter Rumer after she hit the red carpet recently in a very revealing peek-a-boo dress that showed lots of skin – and her pink panties!

“Bruce was mortified,” said a source close to the 59-year-old action star. “As everyone knows, he’s actually a very conservative guy and doesn’t like to see his daughter parading around in next to nothing.”

Insiders say Bruce blames Rumer’s mom, his ex-wife Demi Moore, for the clothing catastrophe at the April 22 Elle Women in Music concert celebration at the Avalon Theatre in Hollywood.

“Bruce belives his ex should have been a better role model to their kids,” revealed the close source. “If she had been, Bruce is convinced that Rumer wouldn’t be exposing herself and causing him ridicule.”

As The ENQUIRER previously reported in 2012, Rumer, now 25, would party in Los Angeles with her mom, and cougar Demi even chased after her daughter’s young male actor friends.

Rumer – who was present at her mom’s Beverly Hills home when Demi had to be rushed to the hospital two years ago– has turned into an eerie reflection of the 51-year-old movie star.

And her recent shocking lack of modesty continues to raise eyebrows.

During the Elle magazine event, Bruce and Demi’s oldest daughter strutted her stuff in a risque black outfit with see-through cut-outs on her thighs. The hip-hugging ensemble also exposed Rumer’s bright pink underwear for all the world to see.

“It was clear that she was trying to get a lot of attention, which she did,” said the source. “But it also bothered her dad. He was terribly embar­rassed and not at all happy about it!

“He basically told Rumer that she was old enough to do what she wanted, and he couldn’t tell her what to wear. But he said that if it was attention she was after, there were certainly other ways to get it, rather than to flash her drawers… and more.”

Bruce has two other daughters with Demi, Scout, 22, and Tallulah, 20, as well as 2-year-old Mabel with his current wife Emma Heming. But he seems most worried about Rumer.

Said the source: “Bruce doesn’t want to see Rumer turn into another overexposed starlet, like Paris Hilton or Lindsay Lohan.”