The Gunners endued several seasons when star players departed, with Van Persie leaving for United and Fabrgeas for Barcelona.
However, Frimpong believes the loss of talisman Van Persie to bitter rivals United was the harder pill to swallow.
"I think I was more disappointed when Robin went to Man Utd because at that time he was the captain and he was the best player in the Premier League," he said to MetaRatings.
"And losing Robin was much more of a blow than losing Cesc because Robin was bringing goals to the game, he was winning us games.
"He was playing really well for us at the time so I feel like he was a big blow at the time, and more than when Cesc left.
"These things happen in football, and you can't control it. It's something that is difficult for the club when you have players who are on less than a year's contract, they want to leave and you want to make money; it makes sense."