United States forward Clint Mathis had put the Americans into the lead in the 24th minute with a sweetly-struck shot.
But South Korea staged a spirited comeback and scored a deserved equaliser through Ahn Jung-Hwan with 12 minutes to go.
Goalkeeper Brad Friedel made a series of stunning saves to keep the Americans in the match, including a brilliant stop to deny Lee Eul-Yong from the penalty spot just before half-time.
Arena was delighted his side came away with a point, acknowledging the hostile atmosphere of the home crowd.
He said: "It was a big day for the people of Korea and playing under these conditions in front of 60,000 of their fans it was a good result.
"To be standing here with four points after two matches is a very good thing.
"Friedel was clearly the man-of-the-match," Arena added.
They put us under a lot of pressure in the second half and it's hard to withstand that pressure
USA keeper Brad Friedel
Friedel saved brilliantly from the penalty spot in the 40th minute after Jeff Agoos made a clumsy challenge on Hwang Sun-Hong.
Friedel dived to his right and parried Lee Eul-Yong's effort away, and Kim Nam-Il sent the rebound wide.
"I felt that he was going to go that way for some reason," Friedel said.
"Who knows why?"
The Blackburn keeper also praised the fighting spirit of the South Koreans, who kept him busy throughout the 90 minutes.
He said: "You have to give them a little bit of credit, too.
"They put us under a lot of pressure in the second half and it's hard to withstand that pressure."
Both teams can secure a place in the second round with a draw in their final group matches on Friday.
The US play Poland while South Korea face Portugal.