The former Gunners midfielder has criticised the Brazilian left-back after approaching the Dutch forward to swap jerseys at the interval after a poor display at Old Trafford
The Brazilian has come under fire for a poor display at Old Trafford, where the left-back failed to deal with the movement of Rafael and Antonio Valencia throughout the game.
And the former Arsenal midfielder believes Santos should have been concentrating more on the game, and less on securing Van Persie's shirt - especially considering the forward scored after just three minutes.
Questioned by The Sun on Santos' action, Parlour said: "That's a joke. I wouldn't have that. At half-time? He should be concentrating on his game and he was having a nightmare."
The £5.6 million signing from Fenerbache has struggled to hold down a regular place in Arsene Wenger's starting line-up since joining in 2011, and did his future chances no favours as he struggled throughout.
Parlour suggested the 29-year-old should not be played in defence again as he was unable to maintain defensive discipline, which ultimately cost Arsenal: "He can't play in a back four as he gets caught out of position all the time."
Santos' tactical intelligence was questioned as early as the third minute, when he failed to pick up the run of compatriot Rafael, whose cross ultimately found its way to Van Persie and the back of the net.