Baseball commissioner Bud Selig said he would not reverse the call, but would examine expanding instant replay in baseball.
Joyce and Galarraga met at home plate Thursday afternoon as the pitcher presented the umpire with the Tigers' lineup card. Joyce shook hands with Galarraga and clapped him on the shoulder.
There were some cheers when Joyce appeared at Comerica Park. There was a smattering of boos when he was introduced.
Joyce has admitted missing a call at first base Wednesday night on what would've been the final out, ruling Cleveland's Jason Donald safe. The veteran ump personally apologized to Galarraga after the game and hugged him.
Joyce showed up to work Thursday looking as if he hadn't slept. He appreciated the outpouring of support from umpires, family and friends but lamented strangers lashing out at his wife and children.
"I wish my family was out of this," Joyce said, holding back tears as he spoke nearly two hours before the Indians-Tigers series finale. "I wish they would direct it all to me. It's a big problem. My wife is a rock. My kids are very strong. They don't deserve this."
Tigers general manager Dave Dombrowski said before the game the team would not ask MLB to overturn the call.
Tigers manager Jim Leyland said MLB gave Joyce the option to not work Thursday's game, but Joyce chose to stick with his job behind the plate.
The fans gave Galarraga a loud ovation in a brief ceremony before Thursday afternoon's game started, during which General Motors surprised the pitcher with a 2010 Corvette convertible.
The instantly infamous play, which had social networking sites abuzz, will add to the argument that baseball needs to expand its use of replays. As of now, they can be used only for questionable home runs.
It's rare for an umpire to acknowledge a mistake in one of the few sports that relies heavily on the human eye, but Joyce did to reporters and later to Galarraga.
"It was the biggest call of my career, and I kicked the [stuff] out of it," Joyce said, looking and sounding distraught as he paced in the umpires' locker room. "I just cost that kid a perfect game."
Leyland was livid during the game when he charged out of the dugout to argue the call and got in another heated discussion with Joyce after the final out.
Later, though, Leyland tried to give Joyce a break.
"The players are human, the umpires are human, the managers are human," Leyland said.
Galarraga bitterly sipped a beer minutes after the blown call
negated his place in baseball history. An apology and hug changed
Joyce asked for a chance to personally apologize after the Tigers beat the
Indians 3-0, which Galarraga appreciated.
"You don't see an umpire after the game come out and say, 'Hey, let me tell you I'm sorry,' " Galarraga said. "He felt really bad. He didn't even shower."
Galarraga, who was barely known outside of Detroit a day ago, and Joyce, whose career had flourished in relative anonymity, quickly became trending topics on Twitter. At least one anti-Joyce Facebook page was created shortly after the game ended and firejimjoyce.com was launched.
"I worked with Don Denkinger, and I know what he went through, but I've never had a moment like this," Joyce said.
Denkinger didn't have to deal with the wrath of fans on Twitter or Facebook. Denkinger helped tilt the 1985 World Series by blowing a call as a first base umpire, and that one incident followed him throughout his career.
Joyce has been calling balls and strikes and deciding if runners are out or safe as a full-time major league umpire since 1989. He has been respected enough to be on the field for two World Series, 11 other playoff series and a pair of All-Star Games.
The split-second decision he made probably will haunt him for the rest of his career.
Joyce emphatically signaled safe when Donald clearly didn't beat a throw to first base for what would've been the last out, setting off a chorus of groans and boos that echoed in Comerica Park.
Chuck Klonke, the official scorer Wednesday night with nearly three decades of experience, said he would not change the disputed play to an error from a hit to give Galarraga a no-hitter.
"I looked at the replay right after it happened, and Miguel Cabrera made a good throw and Galarraga didn't miss the bag so you couldn't do anything but call it a hit," Klonke said Thursday morning. "I watched the replay from the center-field camera, which some people thought showed Galarraga might've bobbled the ball, and I didn't see it that way at all. I have 24 hours to change a call, but I wouldn't consider it.
"End of story."
The story has transcended sports, becoming a topic on NBC's "Today" show Thursday morning and among parents dropping off their kids at the bus stop.
Galarraga was vying for the third perfect game in the majors this year, including Roy Halladay's gem last Saturday night. He seemed to do his job for the 27th out along with first baseman Cabrera on a play teams work on often in spring training.
Donald hit a grounder in the hole between first and second, Cabrera fielded it and threw to first, where Galarraga caught the ball at least a step ahead of Donald, replays showed.
"I feel sad," Galarraga said.
Cabrera said he didn't want to talk about it and Donald answered questions from reporters after a long soak in the tub.
"I didn't know if I beat the throw or not," Donald said. "But given the circumstances, I thought for sure I'd be called out."
The Tigers huddled around one of the two big-screen televisions in their clubhouse, standing stoically and silently as the play was shown over and over.
"I know I played in a perfect game," Detroit shortstop Ramon Santiago said. "In my mind, on June 2, Armando Galarraga threw a no-hitter. I'm going to get a ball signed by him."
Information from The Associated Press was used in this report.