The 42-year-old actor - who is renowned for his womanising ways - briefly dated the actress last summer during her split from now-husband Justin Timberlake, and Gerard regrets not putting more effort into the relationship.
A source told website RadarOnline: "Gerard doesn't have many regrets but not treating Jessica with the respect she deserved while they dated is one of them.
"He genuinely believes she was the one that got away. Jessica liked Gerard a lot, she was into his boyish nature, but she wanted something more serious. She was ready to settle down. That's why after getting close on the set of 'Playing for Keeps' back in 2011, their relationship soon fizzled out."
However, Jessica is now happily married to Justin and she recently said how their brief split made her realise what she wanted in life.
She said: "I needed to be alone for a while. It gives you a lot of strength, a lot of confidence, too, because it means you know that... any decision you make is an educated one, not just an emotional one.
"You make your own choice about whether to step back into a relationship or whether to go in a different direction."
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