The Irish side need to defeat Italy in Lille to have any hopes of qualifying for the last 16 of the competition and right-back Coleman is holding hope of achieving just that.
The 27-year-old used Ireland's shock win over Germany in the qualification stage to emphasise that Ireland can achieve the feat on Wednesday.
He said: "We don't have to look too far back. That night in Dublin, Shane Long's goal, it was a memorable night for us all.
"We know that when it all clicks for and we stick together for the 90 minutes and we don't lose concentration that we are capable of beating big teams.
"I do genuinely believe that there's a big result left in us in this group."