Van Persie has joined rivals Manchester United while Song has moved to Spanish giants Barcelona.
"It is a big mistake to sell them - they were the most important players last season," Eduardo told BBC Sport.
"But they have other quality players to stay as a big club at the top."
"Every player comes to Arsenal as a simple player and Arsenal make them into a big player," Eduardo continued.
"But they can't keep everyone together to fight for titles. Every year it's similar - they lose players, buy players, make them class players and the next year they sell again. They are always in the same place."
"Van Persie and Song were the key players last season," Eduardo continued. "They held the team. When you lose two players like that, your chance of finishing in the top four is less.
"But Arsenal still have a good team and I'm confident they will do well. Last year when they lost Nasri and Fabregas, everyone thought they would not finish in the top four but they did.
"When the season finishes, we'll see if it was a mistake or not. It's very sad to lose two big players like that but we must respect the new players and believe they can keep Arsenal at the top."