In a statement released Tuesday, Jenny Stone also thanked everyone who has reached out to help her family since her husband, 39-year-old Shannon Stone, died Thursday night.
Among those mentioned were team president Nolan Ryan and a man who helped care for young Cooper the night his father died, and then visited the grieving family Sunday.
"We are also thankful for Nolan Ryan, Josh Hamilton, the Texas Rangers, the Rangers fans, and all baseball fans, which have showed such concern and compassion," Jenny Stone wrote in her first public comments. "While I was certainly surprised to hear Nolan Ryan on my phone on Friday morning, I was not surprised that he would act just like we all see him, as a true Texas gentleman. Josh Hamilton remains Cooper's favorite baseball player, the Texas Rangers will always be our team, and baseball will always be our favorite game. ... Shannon loved going to watch the Rangers and he loved Cooper. And, at the very end, he lived life to its fullest, doing something he loved."
Stone lost his balance reaching for a ball thrown by Hamilton -- Cooper's favorite player -- and fell headfirst 20 feet onto concrete. He died an hour later.
Hamilton, in Phoenix for the All-Star Game, said he plans to reach out to the Stone family at some point.
"Obviously, I want it to be personal, face to face," he said Monday. "I'd love to know what kind of man Mr. Stone was and just meet his wife and his little boy and see where it goes from there. .. Nothing we can do is going to bring him back. But the organization can take care of the family and see that everything is going in the right direction."
Two nights after Stone's death, Hamilton hit a game-winning, ninth-inning home run for the Rangers, a release of sorts for a man who was once addicted to drugs and lives with an abundance of Christian faith. He was simply tossing the ball toward a fan who had a young boy with him.
"Just a random act of kindness turned tragic," Hamilton said. "It just lets you know how quickly life can change, just in a blink of an eye, that quick."
Stone was remembered during ceremonies in Brownwood on Sunday and Monday. The memorial drew about 1,000 people, including firefighters, police and other emergency personnel from across the state, as well as Ryan.
"Shannon was truly a great husband, father, son, brother, uncle, firefighter, and friend," Jenny Stone wrote. "While we have been overwhelmed with sadness by his death, we have also been overwhelmed by the outpouring of support and sympathy that we have received, from complete strangers as far away as New Zealand, to the former president of the United States of America (George W. Bush, who was at the stadium that night), to our closest friends and family. ... We will never forget all the firefighters and policemen and women and hospital staff who were there that night."
Baseball Commissioner Bud Selig says major league teams are reviewing stadium safety.
"It was a horrible accident, heartbreaking, almost beyond comprehension," Selig said Tuesday during a question-and-answer session with the Baseball Writers' Association of America.
"Each team determines its own ballpark safety features based on local laws.
"Maybe there's some things they can or can't do," Selig said. "Common sense should always take over in this situation."
Information from The Associated Press was used in this report.