Former Minnesota Gov. Jesse Ventura said Wednesday his successful lawsuit against the estate of late Navy SEAL sniper Chris Kyle was about "the truth" and that he has no plans to reach out to Kyle's widow, who is the executor of the Kyle's estate, now that the trial is over.

"All I wanted to do was clear my name, and it has nothing to do with a widow or anything like that," Ventura said on "CBS This Morning" during his first post-trial interview.

The dispute revolves around the description of an alleged incident in Kyle's book, "American Sniper," in which the former SEAL claimed he punched Ventura in 2006 after the former governor said the SEALs "deserved to lose a few" in Iraq.

"I would have been a big-time loser had I not pursued the lawsuit, because ... the whole story was fabricated," Ventura said. "I was accused of treason, which in the military is the death penalty."

Before he was killed at a Texas gun range by a fellow veteran last year, Chris Kyle delivered testimony that the story was true. Taya Kyle, Kyle's widow, has also maintained through her legal team that she believes the story was true.

John Borger, an attorney for Kyle's estate, told The Associated Press that Taya was "surprised and upset" when she learned of the $1.8 million verdict against the estate. The lawsuit was filed before Kyle was killed.

Ventura has also said he is upset because he is a former Navy SEAL and Kyle's claim hit him personally.

"I can't go to a SEAL reunion anymore," Ventura said. "That was the one place that I always felt safe. I can't go there anymore. I would be looking over my shoulder now wondering who's going to come after me next. And so, don't think I come out of this unscathed."

Much of the criticism against Ventura has centered around the size of the verdict against Kyle's estate, which is providing for his widow and two children. Ventura said that criticism doesn't bother him.

"Taya Kyle had all of her attorney fees paid by insurance. I did not. I incurred two-and-a-half years of lawyer fees that I have to pay to clear my name, and she had insurance paying everything for her," Ventura said on "CBS This Morning." "It was me against an insurance company."

Ventura said he will use his winnings to pay his lawyers' fees.

When asked why he thought Kyle might have made up the tale of the punch-out, Ventura called it a "sea story."

"In the Navy it happens all the time," Ventura said. "One sailor lies to another sailor. That second sailor then tells the story three more times, and all of the sudden, the sea story becomes the truth. They were drunk. They were drinking heavily, and it was just a story that happened in another bar and erupted six years later."

The dispute over Kyle's book may not be over, either. Ventura said on "CBS This Morning" he plans to "visit" the book's publisher, HarperCollins.

"They published the book and did no due diligence to find out if the story was true," Ventura said.

EDITOR'S NOTE: After Ventura appeared on "CBS This Morning," HarperCollins released a statement saying it was removing the passage about the former governor from "American Sniper."