"It was easy for me to slot into this dressing room, it is similar to Iceland," the 25-year-old told British media.
"We're talking about the spirit. Everybody gets along, everybody's mates and set for the same goal. That's important in a team.
"Everybody has to be on the same ball in a team you can say are labelled underdogs. Everybody has to know their role in the team - and that's definitely true in both cases."
Gudmundsson, who joined Burnley from Charlton Athletic in the transfer window, said Iceland had their sights set on qualifying for the 2018 World Cup.
"We want to go to Russia as well, but we're in a tough group, the only group that has four teams from the Euros. There's a bit more respect for us," he said.
"Teams will look at what we can do, but we will play the same, we won't change. It will be hard to top the Euros, but you have to have a goal to reach for, because if you're happy with that, then you won't go anywhere."
Burnley, who have won just one of their five league games this season, host Watford on Monday.
(Reporting by Nivedita Shankar in Bengaluru, editing by Ed Osmond)
