Puncheon's weak headed backpass towards goalkeeper Julian Speroni was seized upon by Southampton striker Jay Rodriguez and he took full advantage of the mistake to score.
Former Southampton man Puncheon admitted his mistake proved hugely costly to Tony Pulis' struggling side.
"I'm very disappointed. I'm disappointed with myself, the mistake I made on the halfway line," Puncheon told the South London press.
"You've got to be honest with yourself. If you can't be honest with yourself, you're never going to get nowhere.
"When the ball came I didn't actually see Jay to my right. I headed it and then when I saw him I tried to recover - I nearly got there but I couldn't.
"Jules (Speroni) has done his best and Rodriguez has done his best. It's just one of those unfortunate things.
"But it's football. There are other things we could have done to win the game and we haven't done that."
The defeat leaves Palace just two points clear of the drop zone and Puncheon admits the games are running out if they are to secure survival.
"The games are getting thinner now. We've got 10 games left and we've got to get points," added Puncheon.
"We've got to concentrate on us, worry what we do and try and get the points on the table."