Koeman, who scored Barcelona's winner in the 1992 European Cup final at Wembley and also won it with PSV Eindhoven, however said Arsenal's lack of experience could count against them.
"They are a fantastic team with lots of quality and make many chances," Koeman told reporters after his first defeat against Arsenal as a coach.
"But they are also a very young team and they maybe lack the experience that say Chelsea and Barcelona have when it comes to the latter stages.
"But that does not mean they can't go a long way in the competition because in knockout it's very close and it's just two matches. They will be one of the teams that can go far."
Koeman described Arsenal captain Cesc Fabregas, who scored twice, as one of the best midfielders in the world.
"He is a great footballer," Koeman said of the Spaniard. "He's fabulous player and very important for Arsenal.
"He was involved in nearly everything but they have many players who really don't need many chances to score."
Arsenal manager Arsene Wenger also praised Fabregas, who was substituted with a tight hamstring, but pointed to the wealth of attacking options at his disposal.
"We had (Nicklas) Bendtner, (Theo) Walcott, offensive players who were not available," Wenger said.
"Denilson too, while Eduardo and Rosicky did not start. Vela too. That is why I was amazed when people said 'buy buy buy!'
"(Andrei) Arshavin was outstanding today because he gave the ball every time at the fraction of a second you wanted him to give the ball. That's top, top quality."
Despite a four-point lead in Group H with just two games remaining, Arsenal are not yet guaranteed to be in the knockout rounds and Wenger is keen not to raise expectations, although he is clearly a happy man.
"Let's focus on ourselves and be as good as we can.
"If we meet somebody who is better, we will see. At the moment it is more important for us to focus on how we want to play and we have played the game tonight like we love."
