He's "very disappointed," though, that the newspaper "wrote a story that was completely false and unsubstantiated," Kraft said in an interview with The Associated Press.
"I must compliment the Boston Herald for doing what is unprecedented in terms of recognizing their error in a major way," Kraft said. "I'm really delighted with that, but I wish it never happened."
The apology came a day after a meeting between NFL commissioner Roger Goodell and Walsh produced no major revelations about the team's videotaping procedures.
"I think I speak for all Patriot fans," Kraft said. "We're relieved that this is over and you see that this is nonsense and we were unfairly accused and we're moving on."
Walsh told Goodell he did not tape the walkthrough and had no knowledge that any other Patriots employees did so, Goodell said. The commissioner also indicated he considered the investigation over after meeting with Walsh on Tuesday.
Kraft said he didn't think the investigation that began then would leave a lasting stain on the club.
"I was unhappy with what transpired in the fall, the actions of some of our employees, and we were penalized severely for that," he said. "We said back in September that we had disclosed all of our actions as an organization to the league. You can see this is true."
"The erroneous story really led to a second round of inquisitions after September, and it really was a distraction. The sad part (is) that it took away from an 18-0 Super Bowl season."
The Herald's story cited unidentified sources and was released Feb. 2.
In the apology, published in the newspaper's Wednesday edition and posted on its Web site, the Herald said the story was based on sources "it believed to be credible."
"We now know that this report was false, and that no tape of the walkthrough ever existed," the paper wrote.
"We should not have published the allegation in the absence of firmer verification. The Boston Herald regrets the damage done to the team by publication of the allegation, and sincerely apologizes to its readers and to the New England Patriots' owners, players, employees and fans for our error."
The newspaper featured a front-page headline reading: "Sorry, Pats." It placed the three-paragraph apology on the back inside page of the newspaper.
Copyright 2008 by The Associated Press.