The defender started and played the full 90 minutes in Switzerland's narrow 1-0 opening game win against Albania in Lens on Saturday and admits that emotions were running high in the Group A encounter.
Both sides have a number of players with the other nation's heritage, while the match also had brothers Granit and Taulant Xhaka facing each other for the first time in European Championship history.
"It was a very tough game", Djourou told Goal on behalf of Meet A Star.
"We were playing against an aggressive team because we have so many players with Albanian roots in the team. It was a very emotional game - one where we had to keep our cool. We did that and managed to come out with the three points even though it wasn't the best game.
“We knew the most important thing in the competition is to win the first game.”
Switzerland joined France by getting their Euro 2016 campaign off to the perfect start with victory in their first Group A clash and Djourou believes Switzerland have enough about them to go far in the tournament.
"We know that we have the quality,” he continued.” It's important to start well in the competition and then march on. We have to be ready to get the three points in this game [against Romania on Wednesday] and then who knows how far we can go. The first test is over, we have to analyse. I believe we can go as far as possible."
Granit Xhaka was named Man of the Match for the Swiss following their win over Albania and Djourou believes his fellow countryman has everything it takes to succeed at Arsenal and will thrive with the midfield competition ahead of him.
Djourou added: "I think Granit has a lot of talent. He showed [against Albania] that he can bring his class and qualities to Arsenal.
“He's a very aggressive player and he can be a very key player for the club. Arsenal have so many good players in that position. Don't forget that there's also Jack Wilshere, Aaron Ramsey, Francis Coquelin and Santi Cazorla. It will be good to have some competition because he's a great player.
"Next season is going to be more open [in the Premier League] and harder to win the league because teams are going to get new players, new managers, new ideas and philisophies. Arsenal has always been thereabouts and in the top four so hopefully it will be their year."
Meet A Star is a brand new international TV show based around a free online competition offering a unique experience prize for 2 that comprises of flights/travel, luxury accommodation and an exclusive meet & greet with a celebrity from the world of sport and entertainment. Entrants enter online through our unique web portal www.meetastar.com. Other stars in the series include Manchester City and France star Bacary Sagna, French open champion Stanislas Wawrinka and Borussia Dortmund record breaking striker Pierre-Emerick Aubameyang.