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Ballack claimed the goal was 'lucky' - just as Germany were 'fortunate' not to find themselves behind when Robbie Keane headed only inches past the right post early in the match.
The Germany captain said: 'They are a very good team and they were very strong, especially at the beginning. We did not start well and were lucky not to fall behind early. But after a while we also carved out a few opportunities so we simply had to stay patient.'
Ireland survived a German onslaught midway through the first period when Miroslav Klose, Ballack and Podolski all threatened from promising positions.
The Germans created only a handful of chances in the second half but remained firmly on the front foot throughout.
Ballack said: 'At some point the ball just hits the back of the net and you get rewarded. That is what happened (against Ireland).'
'Ireland are no pushovers at all. This was hard work and the victory did not come easy. But we played very disciplined. We kept a clean sheet with a newly-arranged defence. At the end of the day we deserved to win but it did not come easy at all,' he added.
Ballack, who was playing in only his second competitive match of the season after a hip injury had delayed his Premiership debut with Chelsea, believes the win will give Germany the 'confidence we need' to progress out of a group which also features Czech Republic, Cyprus, San Marino, Wales and Slovakia.
'This tough match really helped us to gain some stability,' the midfielder said.
'We might not have created too many chances, but we're very happy to kick off the campaign with three points. In the qualifying campaign all that matters is a win.'