Given is Ireland's most capped player with 124 caps to date, but he has now confirmed that Monday's game with Italy will likely be his last.
The Aston Villa keeper has come in for some criticism for his performances in Poland, with Ireland already out before their final group game.
"I think it might be time to step aside and let somebody else come into the side," he said.
"It's all a bit raw at the moment because we've lost an important game but at some point I'm going to have to make a decision."
Given was speaking in the aftermath of their 4-0 drubbing at the hands of Spain and he admits they have never come across a side as good before.
"I don't think any team has ripped us apart like Spain have," he continued.
"It's a credit to the way they play, the system, the way they pass and move and the mobility.
"They're a fantastic team. We said before the game that we knew what was coming. It's all very well having a gameplan but you've got to implement it and we didn't do that well enough.
"Spain are a great side, they have so much movement off the ball, pulling you one way to create space for someone else to come into.
"They're incredibly hard to defend against. I think they showed in the second half why they are the defending champions and they're going to be hard to beat again."
Meanwhile, Given has also hit back at former Ireland captain Roy Keane who condemned their performance at the Euros claiming they had turned up 'just for a sing-song'.
"I'm sure the fans have come for a sing-song, but the players certainly haven't. Why shouldn't the fans enjoy themselves? They've waited a long time to get to this stage," he said.
"But we certainly haven't come along for a sing-song.
"We didn't come here just to have a good time, we came here to try and get out of the group stage and progress in the competition.
"Unfortunately, we weren't good enough but you can't say we weren't trying or that we didn't take it seriously.
"Any 4-0 defeat is tough to take, no matter who the opposition are - and this hurts. They're a fantastic team, we said before the game that we knew what was coming."
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