And Gunnarsson believes Iceland are comparable to Wales, who will face Portugal in the semi-finals.
The Nordic minnows have also defied pre-tournament odds by downing England to set up a last-eight clash with hosts France and Gunnarsson therefore believes his side have a lot in common with Chris Coleman's charges.
"Like we knew before the tournament, [Wales] were not favourites to reach that far and we weren't either," Gunnarsson told a press conference on Saturday.
"It's a joy to watch and I think Wales are a force to be reckoned with. They have got a good squad, good players and tough togetherness.
"They are showing a great attitude and desire to win football matches and it's something we can learn from them. We are also quite similar to them in that respect."
France right-back Bacary Sagna recently compared Iceland's Euro 2016 run to Leicester City's unlikely Premier League title triumph, but Gunnarsson insists Iceland are not trying to replicate the success of any other team.
"We're not trying to be like Leicester," Gunnarsson said. "Leicester have done a fantastic job. They were the underdogs in the Premier League with all that money in there.
"We are not trying to be like any other team. We're just Iceland and it is our identity how we come towards the game and how we approach it. It's been fantastic to be part of this squad.
"Playing against bigger teams with the best players in the world is always going to be tough, but you're in this to test yourself. It's going be a big test for us tomorrow, but we're ready for it."
"It's always the most fun to play against the best players," Gunnarsson said. "He is clearly one of the best players.
"He is one of those players who is really superb. It's going to be a hard fight and I am ready to battle against anyone. It's been going alright until now.
"It's another game that we are ready for tomorrow."