Giovanni Trapattoni's men lost 2-1 in World Cup Qualifying Group C to Sweden in Dublin on Friday evening and speaking afterwards Dunne couldn't hide his disappointment.
Dunne said: "It's a big blow to lose. We know we needed four points from the next two games.
"We were flying in the first half but if you gives quality players time and space they will punish you and that's what they did."
The Republic travel to Austria on Tuesday knowing that they are now reliant on other results going their way.
Dunne added: "It's going to be difficult but we have to believe."