Cowen, who has been on the defensive himself since taking over just before Ireland's "Celtic Tiger" boom tumbled into recession, is hoping a moment of individual brilliance will send the Irish to next year's finals in South Africa.
"Mr Trapattoni has provided us with a team and a system that means we don't leak many goals, we are good defensively," Cowen said on a video posted on governing party Fianna Fail's website.
"We're relying then on some of the individual brilliance of our midfielders and forwards to produce on the day," he added.
Trapattoni's resolute side were unbeaten in a qualifying group that included world champions Italy and Cowen questioned whether France, who surprisingly finished behind Serbia in their group, matched Ireland's cohesion and teamwork.
"They (France) are a good side, they've got a lot of good individual players but whether they've got the same sense of teamwork and cohesion that we have, and the consistency that we built up during qualification, remains to be seen," Cowen said.
"The lads have a lot of self-belief that they can do the business and let's hope they do."
Ireland host France in Dublin on Saturday with the return leg four days later. The winner qualifies for next year's finals in South Africa.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
