The post-mortem into Ireland's trip to Poland and Ukraine, where they failed to pick up a point from their three group games, was set to continue on Wednesday, amid fears Giovanni Trapattoni's men embarrassed themselves on their return to the biggest stage.
Given, one of few survivors from their previous major tournament at the 2002 World Cup, admitted it was hard to find positives after they conceded nine times - scoring just once - during their three Group C matches.
The 36-year-old, who is contemplating retiring from international football having won a record 125 caps, said: "We've just lost three games, so positives are thin on the ground.
"We came here before the tournament expecting to do better.
"Things are hurting at the minute, but when you look at the bigger picture in a few months' time then maybe you'll see some positives."
Aston Villa goalkeeper Given admitted he could not have envisaged such a dismal display at Euro 2012.
"I don't think anybody did," he said after Monday's final group defeat to Italy.
"We went into the tournament with plenty of confidence and looking forward to it.
"But it's just shown the standard of teams you're up against when you get to major finals.
"Especially Spain. We all know how they played and even Croatia were a very strong team as well.
"You know when you get to the finals, you're up against the elite players and the elite teams."
Given denied mental fragility had cost Ireland.
"I think the biggest problem we had in both the first two games was to concede such an early goal," he said.
"That put us back and everything you train and work for, game plans and things, kind of go out the window.
"You concede a goal after three minutes and, in the next game, you concede a goal after four minutes, so that was very tough to take."
The former Newcastle and Manchester City star refused to make excuses about his own error-strewn performances, despite carrying an injury days before the tournament.
"I only trained two days before the very first game so that wasn't ideal, I suppose," he said.
"But my sharpness? I don't know.
"I'm not making excuses.
"I was 100% fit to play, so when you cross the white line, it's over to you."
He added: "It's been a tough few weeks and it'll be tough going home now to see the people back home.
"It'll be tough because we've brought nothing back home with us."
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