The former Manchester City and Aston Villa defender is hoping to remain involved with the Boys in Green for the forthcoming Euro 2016 qualifying campaign
The Queens Park Rangers defender returned to the Ireland team for the game against Kazakhstan after missing the 3-0 defeat against Germany in Cologne on Friday through suspension and was pleased to finish the campaign with a victory.
"It's a long way away but I'd like to be a part of [Euro 2016]," Dunne told reporters after Ireland's 3-1 victory over Kazakhstan. "I've worked hard to get back. I understand that teams change over time. It would be great to be part of it, but if not, I've really enjoyed myself.
"It was a good performance from everyone [against Kazakhstan]. It wasn't the best of campaigns but we finished it well.
"We've got a squad that's more experienced and comfortable at this level and I think in the next campaign or the one after we can start looking to qualify again," he added.
The 33-year-old defender said that it was "enjoyable" to work with interim boss Noel King, but indicated that the Football Association of Ireland (FAI) should appoint a new manager "as quickly as possible."
"It's been an enjoyable few days working with Noel, and I think all the lads really enjoyed it," he said. "You'd like to see a new manager in as quickly as possible."
With the association no closer to appointing a permanent successor to Giovanni Trapattoni, King could potentially lead the Boys in Green for friendlies in November, but the former Derry City boss refused to be drawn on speculation.
"I work for the FAI, I'm delighted with my job with the Under-21s. If the FAI want me to do something, they'll talk to me. If they don't, that's okay," he said.