Spiller, 29, signed a four-year, $16 million deal with the Saints in 2015. They wound up paying him $9 million for a total of 13 games played.
He told ESPN's Josina Anderson of his release that he "didn't see it coming."
"It's the first week, but I guess that's why you have to expect the unexpected. But you know what, I leave on good terms," he said.
"This organization really believed in me during free agency. They gave me another opportunity when my contract was up in Buffalo. I have nothing but good relationships that I have built here. It's a first-class organization that gives the players everything they need to be successful. So, I definitely don't have any hard feelings."
He said he now will "wait for the next right opportunity."
Spiller was inactive in Week 1, with Saints head coach Sean Payton explaining that it was a game-plan decision to go with veteran runner-receiver Travaris Cadet ahead of him. A league source confirmed that it wasn't health-related.
Payton explained that the Saints waited before releasing Spiller because they looked into a potential trade. They ultimately needed the roster spot after an injury to cornerback Delvin Breaux.
Payton called Spiller a "phenomenal, phenomenal" person and teammate. He said the main issue was Spiller's inability to fully return to peak form after his 2015 knee injury.
"I think he's gonna have another opportunity sooner than later with another club. And the window, I know, in this building is not permanently closed," Payton said. "Obviously last season was frustrating because he dealt with the knee injury in training camp. And I think he's ahead of where he was a year ago and has gotten better than where he was a year ago. And yet, it just became a challenge for us when we were looking at (game-day) actives and roles. And that was really it."
Spiller's run in New Orleans was extremely disappointing. He had just 112 rushing yards, 239 receiving yards and two touchdowns last year while struggling to overcome a minor knee surgery he underwent during training camp. Eventually, the Saints shelved him for the final two weeks and replaced him with Cadet.
Things seemed to be going better this year, with Payton saying Spiller showed progress and some "juice" during training camp and the preseason. The Saints seemed committed to him after allowing his base salary of $1.7 million to become fully guaranteed in March.
However, it seemed likely that the Saints wouldn't keep six running backs all year -- and Cadet seems to be their change-of-pace back of choice.
Cadet had three catches for 14 yards and a touchdown on seven targets Sunday and added one carry for 1 yard.
The Saints now have more than $40 million in "dead money" counting against their salary cap -- by far the most in the NFL (the Cleveland Browns are second at $28.1 million, according to ESPN Stats & Information). That number includes their other big free-agent signing from 2015, cornerback Brandon Browner, among several others.
Spiller will count $4.5 million against this year's cap, then another $2.5 million next year.
Spiller was drafted by the Buffalo Bills in the first round of the 2010 draft at No. 9 overall and made the Pro Bowl with a breakout year in 2012 (1,244 rushing yards, 459 receiving yards). He has 3,433 rushing yards, 1,434 receiving yards and 22 total touchdowns (including kick returns) in his career.