The Bournemouth midfielder was forced to pull out of the squad following the 1-1 draw with the Netherlands, but is still eyeing success with the national team.
Bournemouth's Harry Arter in action with Arsenal's Aaron Ramsey
The 26-year-old was named in boss Martin O'Neil's provisional squad for the tournament in France, before picking up a suspected thigh injury before the side's recent friendly with the Netherlands.
Despite completing 90 minutes of the 1-1 draw at the Aviva Stadium, Arter was forced to pull out of Ireland's final warm-up match with Belarus, with results of a subsequent scan ending his hopes of appearing at the tournament.
But despite his disappointment, Arter is still hopeful of making an impression at international level, having already been backed by assistant boss Roy Keane as a future Ireland star.
Republic of Ireland's John O'Shea celebrates scoring their first goal with Robbie Brady and Harry Arter
The English-born ace has returned that praise, hailing the strong working relationship he shares with both Keane and O'Neill, and says he is hungry to add to his tally of two international caps.
Talking about his withdrawal from the squad, Arter said: "I had a good 20-25 minute chat with Roy and it was really beneficial for me. I’ll keep our conversation private but I have huge respect for him, I grew up admiring him and obviously I’d listen to anything he had to say.
"He said some nice things in the press afterwards about me which was nice to read and I had a similar chat with Martin O’Neill.
"Again, I won’t say what he said but I'm hungry to get back playing for my country and while I'm disappointed to miss out, I'm looking forward to the future."