Martin O'Neill's side started their Euro 2016 qualifying campaign with a victory, claiming all three points in Tbilisi thanks to McGeady's sensational 90th-minute clincher.
The Everton winger had already netted once, rounding off a counter-attack with a cool finish midway through the first half.
Tornike Okriashvili levelled for the hosts seven minutes before the break with a spectacular effort from distance, but McGeady proved Ireland's hero.
He told Sky Sports: "Three points are massive, it sends a statement to the rest of the group.
"We've come to a difficult place like Georgia and got three points. We played okay, but we know we can play a lot better.
"I think [in] the first half we were the better team overall but Georgia have good technical players, they had half chances and the goal came from nothing.
"It's hard to break teams down away from home. We had half chances, credit to the boys, we got it [the win] in the end."
Manager O'Neill cut a relieved figure after the match, but he made no attempt to hide his joy at coming away from Georgia with all three points in his first competitive fixture in charge.
"I'm delighted," he told RTE. "We won the game and it's three points away from home.
"I'm absolutely delighted and so are they [the players]. It's our first game, there was a bit of nervousness in the team.
"Obviously we wanted to try and do well away from home. We didn't know what to expect from them [Georgia].
"We've watched them a lot but until you play the game itself you don't know. At least now we can think about the two games coming up next month [against Gibraltar and Germany]."
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