The Enchanted actress ended her relationship with Robbins in December 2009 after 23 years.
Talking to Reuters, Sarandon revealed that she tried to remain positive about being single despite the difficulties of leaving behind such an important era of her life.
"Of course you feel like a failure. It's a big deal, but again, it's an opportunity to grow. At the end of my first marriage, it was about the loss of ideal, about who you thought this person was. I thought love conquered all and I had to reevaluate everything," Sarandon explained.
"And you need your girlfriends, you need to take long, long walks until you're exhausted and no longer freaking out and you hold on until a new dawn. Then you get another chance," she added.
However, the 65-year-old insisted that she has bounced back from the experience and now feels excited about what the future holds.
"It's been a lot of different things. It's traumatic and exhilarating. The one thing that's been really clear to me is that you have to think of your own life and your relationship and everything as a living organism," Sarandon said.
"It's constantly moving, changing, growing. I think long-term relationships need to be constantly reevaluated and talked about."
Sarandon has previously commented that the nation mourned her split from Robbins, with many people seemingly more upset than she was.
Sarandon's new film, Jeff, Who Lives at Home, was released in US cinemas yesterday (March 16) and will be released in the UK on April 20.
Watch the trailer for the film below: