"I was pretty pissed off about it," Shattenkirk said, according to Stephen Whyno of The Associated Press.
"I think I'm pissed off at myself for not taking advantage of the opportunity to play at home better and give them a reason to make it a no-brainer that this wouldn't be their decision," he added.
The Rangers bought out Shattenkirk last week with two years and $12.6 million remaining on a deal he signed in 2017. The 30-year-old defenseman inked a one-year, $1.75-million contract with the Tampa Bay Lightning on Monday.
Shattenkirk - one of the top free agents available in the summer of 2017 - left money on the table to sign with his hometown Rangers. He hails from nearby New Rochelle, N.Y.
Over his two seasons in the Big Apple, Shattenkirk missed significant time due to both a torn meniscus and a separated shoulder. All told, he appeared in 119 games for New York, registering 51 points.