Denmark qualified for the World Cup following a 5-1 aggregate victory over the Irish in a play-off, with Christian Eriksen's hat-trick ending the hopes of the 'Green Army'.
Eriksen is sidelined from Saturday's game with an injury, but Schmeichel has called for his country to deliver against a 'motivated' Republic of Ireland side.
Speaking to 'Sky Sports', the Leicester shot-stopper said: "It doesn't matter if Christian's here or not, we need to win anyway.
"You take Christian out of any team in the world and you're going to feel it but that's football - it's a chance for someone else to step up and try to stake a claim.
"Christian's a remarkably consistent player. It's a rarity [his absence] but it is testament to how he lives his life; he's professional, dedicated. But we need to weigh in with goals and creativity from all over the pitch.
"We know this will be really tough considering what happened last time. They will be highly motivated to exact revenge. They're going to be looking to set the record straight but we are in no way complacent.
"When it matters we've been really good - apart from the game against Croatia, but that comes down to the luck of penalty shoot-outs. Take the game [in Dublin] -
"In terms of my Denmark career that's definitely up there - getting to a first World Cup was phenomenal and being under pressure - one-nil down - and coming back the way we did was testament to this team; the quality, the spirit, the mental toughness.
"It's a very young team and there are some really good players in that dressing room. We're moving in the right direction but the exciting thing is that there's more to come."