The Welsh, who were seeded in the top group for the first time in their history, will also face Austria, Serbia, Moldova and Georgia in Group D.
And with the Dragons leading their Euro 2016 qualifying campaign ahead of Belgium, Coleman said his side have shown they can be a match for anybody.
He told Sky Sports News HQ: “I’m not really worried too much about the opposition.
We’re up against tough opposition, but I know what we’re capable of and we’ve got a good team.
“We concentrate on ourselves.The Republic of Ireland will be a great test, the atmosphere will be fantastic.
“We’ve got to go to places like Moldova and Georgia which is never easy.
“But as we’ve proven, we’re a match for anyone at the minute. We’ve got nothing to fear, we respect everybody and they are all going to be tough games.”
Wales will face a tricky test against Serbia who handed them a 6-1 thrashing in 2012 in their qualifier for the last World Cup.
But Coleman believes his side have improved since being well beaten three years ago.
“We suffered in the last campaign, I think we’ve grown since then and are a better team now,” the former Fulham boss added.
“We were beaten heavily but we’re a different team now.
“Not to say it will be easy, it’s always tough going to places like Serbia.”
Qualifying for the tournament in Russia will begin in September 2016.