McGinn's 75th cap turned into a night to forget as Scotland let Thursday night's 1-0 first-leg lead slip.
Clarke's side were booed off at half-time and fulltime by the Tartan Army who had sold out the National Stadium hoping to see a performance to keep momentum building towards the World Cup qualifiers. But two first-half goals from Giannis Konstantelias and classy kid Konstantinos Karetsas saw the Greeks overturn Thursday's result in Athens before a third goal just 15 seconds into the second half from Christos Tzolis killed the tie.
Greece now lie in wait again in the race to reach next summer's World Cup finals.
And Aston Villa midfielder McGinn said: "Greece deserved to win and that will maybe give us a kick up the backside for the World Cup qualifiers because we know they're no mugs.
"We obviously played very well the other night to get a result but tonight shows we have to be much, much better if we want to get to a World Cup.
"It's an embarrassing night for us, everyone is flat after it.
"You could feel that in the stadium, we let ourselves down tonight." Scotland had thrown themselves a Nations League A lifeline with impressive wins against Croatia and Poland before Thursday night's win in Athens.
But all that good work was undone on a woeful night in Mount Florida.
McGinn added: "We've had plenty of praise over the past few months.
"We managed to get ourselves into a play-off but let ourselves down.
"We didn't have enough threat in behind, we are all responsible for that.
"We had the gameplan but were too easy to pick up. We started pretty well the first 10 minutes and had a couple of chances.
"But we let ourselves down with the first goal we conceded then the second one straight after that.
"We regrouped at halftime but after that it's the worst possible scenario and situation.
"We have to re...