Heimir Hallgrimsson's side picked up five points from their four games in the autumn international window - but a late 1-0 loss to Austria in Linz has put their promotion on the back foot - ahead of hosting Kosovo on November 17.
Ireland trail Kosovo by a point in the group and need a win in Dublin to overtake them and claim a playoff place.
Parrott has developed into the talisman of Hallgrimsson's team in the las 12 months and the Real Betis forward insists it's all to play for in the final game.
"We came to win. We fell short today, but we still have a big chance on Tuesday, to do what we want to do.
"On another night, maybe we'd have scored two or three goals, that's just how football is sometimes.
"What's positive for us and things that we can take forward is the fact we created so many chances. To be honest, with Ireland teams over the last few years, that hasn't been the case.
"It's a positive for us to take forward and into Tuesday and go and score goals."