Ireland have been draw with Russia, Slovakia, FYR Macedonia, Armenia and Andorra.
‘We will start with the same mentality we had three months ago against France,’ Trappatoni told Sky Sports News.
‘If we begin with the same mentality, we have the possibility to qualify.’
Russia, top seeds in the draw, did not qualify for the World Cup either having suffered a surprise defeat to Slovenia, but Slovakia did.
And Trappatoni admitted the Slovakians could be as big a threat as Guus Hiddink’s team.
‘I think all the groups for me are about equal,’ said Trappatoni. ‘It’s a tough group but other groups are also tough.
‘Russia will be difficult and Slovakia. Slovakia are a technically good team and they are a team with a very tough mentality.’
The groups in full:
Group A: Germany, Turkey, Austria, Belgium, Kazakhstan, Azerbaijan
Group B: Russia, Slovakia, Republic of Ireland, FYR Macedonia, Armenia, Andorra
Group C: Italy, Serbia, Northern Ireland, Slovenia, Estonia, Faroe Islands
Group D: France, Romania, Bosnia-Herzegovina, Belarus, Albania, Luxembourg
Group E: Holland, Sweden, Finland, Hungary, Moldova, San Marino
Group F: Croatia, Greece, Israel, Latvia, Georgia, Malta
Group G: England, Switzerland, Bulgaria, Wales, Montenegro
Group H: Portugal, Denmark, Norway, Cyprus, Iceland
Group I: Spain, Czech Republic, Scotland, Lithuania, Liechtenstein
Topics: Albania, Andorra Group C: Italy, Armenia, Austria, Azerbaijan Group B: Russia, Belarus, Belgium, Bosnia-Herzegovina, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Faroe Islands Group D: France, Finland, FYR Macedonia, Georgia, Greece, Hungary, Iceland Group I: Spain, Ireland get tough draw for Euro 2012, Israel, Kazakhstan, Latvia, Liechtenstein, Lithuania, Luxembourg Group E: Holland, Malta Group G: England, Moldova, Montenegro Group H: Portugal, Northern Ireland, Norway, Romania, San Marino Group F: Croatia, Scotland, Serbia, Slovakia, Slovenia, Sweden, Switzerland, The groups in full: Group A: Germany, Turkey, Wales