Paula Abdul yesterday insisted she is getting a raw deal from people who believe she isn’t smart.

“I am intelligent,” Abdul told CBS’ “Sunday Morning” show.

“Having a brain? That’s a concept, yes, with Paula Abdul. I have a brain.”

Abdul is hosting a new talent show, “Live to Dance,” which debuts this week.

Rumors of her having a substance-abuse problem were also off-base, she said.

“I’ve never had a drinking problem . . . Even though I’ve been in this business for quite some time,” she said.

“I’ve never been drunk in my life. I don’t use recreational drugs. But, I am goofy,” Abdul said.

“And, even the people on ‘Idol’ know that none of that [substance abuse] existed. Ever,” Abdul said.