Jay Beatty, from Lurgan, County Armagh, was offered the chance by the Greek Soccer Federation, after Samaras thanked Jay for his "strength and support" following Tuesday night's World Cup match against Ivory Coast.
The Glasgow Celtic striker scored a last-minute penalty to send his country though to the second round of the competition.
Greece fans were jubilant after the crucial goal, but none more so than Jay, a long-time  Celtic fan.
The Greek football authorities offered the family the chance to travel to Brazil to watch Greece take on Costa Rica on Sunday.
However, the Beatty family had to turn the offer down due to a pre-arranged trip to the United States.
Jay's father, Martin, wrote on his Facebook page: "This morning we got a call with a fantastic offer for us all to go to the World Cup to see the Greece game and Jay's hero, Samaras.
"Unfortunately, we were actually at the airport heading off on our family holiday when we got the call.
"So naturally we were unable to take up the offer and are so gutted, but truly grateful that people would do this for Jay."
The boy made headlines in Greece when the Celtic striker pulled him from the crowd to celebrate the club's Scottish Premiership title win on 11 May.
Jay was also presented with Celtic manager Neil Lennon's league winners medal.
Samaras has remained a favourite of the boy's, to the extent he is supporting Greece in the World Cup in Brazil.
When Samaras scored on Tuesday night, a video of Jay celebrating went viral after his father, Martin, uploaded it to his Facebook page.
Earlier this week, Samaras sent his own message to the young boy during the post-match press conference.
He said: "Jay, I want to thank you for the strength you give me.
"Your smile and your support gives strength to everyone. In the end, I want to say that I'm very, very proud that you're my friend. So I hope to see you soon, buddy."
Despite having to turn down the offer to travel to Brazil, Martin posted a video message on Facebook from Jay to his hero.
He said: "Sammy, I'm sorry I won't be there but I still love you very much and hope you win. Come on Sammy!"
The family of an 11-year-old boy from Northern Ireland have turned down an invitation to the World Cup, after being thanked by Greece striker Georgios Samaras.