Goals from Antonio Cassano and Mario Balotelli ensured that the Boys in Green would leave the competition pointless, while sending the Italians through to the quarter-finals in the process.
"[At] This minute it's tough to take any positives from the tournament, we were beaten three times, we expected to do a lot better before we came here but maybe in few months' time we will look at the bigger picture and draw more optimistic conclusions," Given told reporters. "Of course we improved as players and as a team.
"It's been a tough few weeks for everybody, the squad and me, and especially the fact that we are coming home without any points has been especially tough for us."
The 36-year-old shot-stopper expressed his disappointment at Ireland's latest defeat and acknowledged his part in conceding the first goal, after he spilled a long-range shot onto the post to give away the corner that was duly nodded home by Cassano.
"We played well tonight," he added. "We feel the goals were harsh on us and we should have done something for ourselves.
"The first goal was of course my mistake but it takes a lot of time for the ball to end up in the back of the net and it was also good delivery from [Andrea] Pirlo as well. Cassano is the smallest player on the pitch as well so from that point of view it is disappointing.
"And how it led to the corner was disappointing, again it was my mistake, I should have dealt much better with the shot but with that humid weather it gets a bit tougher. I have to admit that I should have done a lot better, though."
The Aston Villa keeper also commented on the performance of midfielder Keith Andrews, stating that he did not deserve the red card he received in the second half.
"Keith put in a great performance tonight I think, his sending off was a little bit harsh, he showed some frustration on the way off but his display was excellent, as it was in previous games," he added.
The former Newcastle and Manchester City keeper was also coy over his international future, with rumours circulating that this could be his final competitive game for the Republic of Ireland.
"I'm coming back home, I will try to spend some time with my wife and my kids. My decision over the future will be both professional and personal. I will also speak to the new boss [Paul Lambert] at Aston Villa to see how he sees it," he concluded.