Jennifer Lopez says she's sad about her split from ex-husband Marc Anthony but still remains optimistic about love.

"That was my biggest dream, and I really worked hard at it. We both did. Sometimes it doesn't work and that's sad, but I remain an eternal optimist about love. I believe in love," the American Idol judge told Vanity Fair in her first interview since she and Anthony announced their split last month.

"It's still my biggest dream. I am positive -- determined to move forward with my life, bring up my babies, and do the best job I can as a mother, entertainer, and person. I now look forward to new challenges. I feel strong."

Lopez -- who joined American Idol as part of last season's judging shakeup alongside fellow judge Steven Tyler and has reportedly reached a still-unannounced deal to return as a member of the show's judging panel -- told Vanity Fair she loves herself more and is a better person without Anthony by her side.

"I'm a hopeless romantic and passionate person when it comes to love. It's not that I didn't love myself before. Sometimes we don't realize that we are compromising ourselves. To understand that a person is not good for you, or that that person is not treating you in the right way, or that he is not doing the right thing for himself -- if I stay, then I am not doing the right thing for me. I love myself enough to walk away from that now," Lopez explained.

Lopez also said she will always respect Anthony as a professional entertainer.

"I will always respect Marc as a singer and performer," Lopez told Vanity Fair.

"We actually work great together, and he was always very supportive. Together we could make magic and we did. He will always be in our lives. He will always hold a special place in my heart as the father of my children," she added.