Kenwyne Jones was sent off for Saints after a first-half melee before Palace keeper Scott Flinders escaped with a yellow card for an apparent handball.
Gareth Bale struck the bar from the resulting free-kick but Saints did take the lead when Chris Baird headed in.
However, Baird's joy was shortlived when his error gifted McAnuff the ball and he slotted home to equalise.
"Usually when a team plays with 10 men for so long you'd be happy with a draw but I felt we deserved a win.
"We never stopped trying to attack, had more of the possession and the better chances and, but for one mistake, we would have won."
"It looks like Scott just kicked the ball on to his arm. It shouldn't even have been a yellow card.
"He came in at the last minute after Julian Speroni was injured and he had a great game."
Southampton: Davis, Ostlund, Baird, Lundekvam, Bale, Surman (Wright-Phillips 88), Wright, Pele, Skacel, Rasiak, Jones.
Subs Not Used: Bialkowski, Idiakez, Dyer, Viafara.
Sent Off: Jones (28).
Goals: Baird 47.
Crystal Palace: Flinders, Butterfield, Hudson, Ward, Granville, Soares, Fletcher (Reich 46), Kennedy, McAnuff, Morrison (Freedman 66), Kuqi.
Subs Not Used: Wilkinson, Lawrence, Scowcroft.
Booked: Fletcher, Flinders, Soares.
Goals: McAnuff 54.
Att: 30,548.
Ref: R Beeby (Northamptonshire).