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But Belgium's 1-0 win in Galway last night, courtesy of a 68th-minute Maarten Martens strike, now gives them control of the group.
Only a single-goal Greek win away to the Belgians on Tuesday will be enough to see Ireland through and Givens does not expect that to happen.
Should this prove to be the end of the line for this group of players, Givens will look to the future with some of the young attacking talent that he threw on in the latter stages.
He said: 'We had to throw on forward players at the end. We put on Andy Keogh and young Terry Dixon, although it wasn't an ideal place to give him his debut.
'I hope he'll be involved in the next campaign. We've a few younger ones here, the likes of Anthony Stokes was also involved and he's young enough for the next one.'
A changing of the guard looks more than likely, with Givens admitting it would take a miracle for Belgium to go down to Greece.
He said: 'I'd be amazed if they don't beat Greece now. They're a much better side than the Greeks and at home you'd expect them to be even stronger.'
Givens was particularly upset for his side's older players as many of them will not be able to play at this level in the future.
He said: 'Something we stressed is that it could be the end of the road for some of these boys and you can see them staring into the quiet in the dressing room. It's terrible for them.'