Having finished second to Russia in qualifying Group B for the tournament, the Irish must now overcome a dire record in two-legged ties when they head to Estonia in November.
"It is extremely positive for Ireland that we will play the first leg away," the veteran coach said.
"We should not underestimate our opposition, or any team, including Estonia.
"To have made it through to the play-off, they must have quality and mental fortitude.
"Our build-up to this stage of the competition has shown us the importance of organisation, attention to detail, and self-belief.
"That will be vitally important to us as we prepare for these games."
Ireland have featured in five previous play-off series but won only one of them - when they beat Iran to reach the 2002 World Cup.
They will need a second win from six attempts if they are to qualify for their second ever European Championship.
Their most recent flirtation with a play-off ended in acrimony, when Thierry Henry's handball helped France qualify for last year's World Cup at their expense, while they have also fallen foul of Holland, Belgium and Turkey.
Ireland will start their latest attempt to qualify for a major tournament in Estonia on Friday, November 11, with the return leg at Dublin's Aviva Stadium on Tuesday, November 15.
Tarmo Ruutli's Estonia emerged from a group containing Italy, Northern Ireland, Serbia, Slovenia and the Faroe Islands to take second place, and with it earn a first ever play-off berth.
They have never made the finals of a major tournament, and history is not on their side either.
The two previous meetings between the pair have gone the way of the Irish, 2-0 on both occasions in qualifying for the 2002 World Cup, with Richard Dunne on target in each game.