Given and his defence were unable to extend their record of successive clean sheets to nine games on Tuesday night, but Henrikh Mkhitaryan's 62nd-minute strike proved only a consolation as Ireland ran out 2-1 victors over Armenia at the Aviva Stadium to finish second in Group B.
The draw for the play-offs will take place in Krakow on Thursday with Giovanni Trapattoni's men seeded alongside Portugal, Croatia and the Czech Republic.
That means they will face either Turkey, Bosnia-Herzegovina, Estonia or Montenegro over two legs next month, but Given is not too concerned about who comes their way.
Asked for his preference, he said with a smile: "Somebody easy.
"We will just take it on the chin. Whoever we play will know they are in for a very tough game when they come here, and we will give them a tough game at their home place as well.
"Please God, we can get across the line this time and get through the play-offs."
Given, of course, has experienced both the joy of play-off success and the bitter pain of defeat.
He was in the team which saw off Iran to make the 2002 World Cup finals, but suffered the heartache of failure, and not for the first time, in France two years ago as dreams of a return to the biggest stage of all went up in smoke.
At 35, he knows his chances of making another major finals tournament are receding and for that reason, he had no qualms about accepting the good fortune that came Ireland's way on Tuesday night.
Armenia keeper Roman Berezovsky was sent off after 26 minutes for handling Simon Cox's shot outside his area, although replays suggested he was innocent, and that the ball had brushed the striker's arm first.
Add to that Valeri Aleksanyan's 44th-minute own goal and Richard Dunne's second, which he bundled home after substitute keeper Arsen Petrosyan had spilled Aiden McGeady's cross on the hour, and it was difficult to argue fate had not smiled on the Republic when they needed it most.
Given said: "I was a long way off, but it looked to me like handball. But people are then saying it maybe hit him in the chest.
"I don't know, but maybe we are due a little bit of luck. We got a little bit, but we scored a couple of good goals and we are just happy.
"Sometimes you have just got to enjoy it and we will enjoy the victory and we will enjoy getting 21 points in the group.
"It's been a long campaign and hopefully we can finish it off next month."
Trapattoni's men ultimately finished two points adrift Russia, who were swiftly installed as favourites to win the group after it was drawn, but clear of the in-form Armenians and Slovakia.
They did so as a result of victories over Andorra and Armenia in their final two qualifiers, and with Turkey having lost 3-1 at home to Group A winners Germany on Friday evening, that was enough to ensure they were seeded for Thursday lunchtime's draw.
Dunne said: "This whole week has been about getting the points, and that's what we got in the end.
"We knew realistically the play-off was going to be our best shot coming into this week. We thought if we could get six points, then we were guaranteed it, and we have done it.
"It may not have been the prettiest, but we have got the results."
Mkhitaryan's strike might have ended Ireland's run of games without conceding, although Dunne was simply happy that it had not proved costly.
He said: "We were going to concede a goal at some stage. But we had gone eight games without conceding, so if we concede one, the house isn't going to fall in."