Wales international midfielder King, who is in talks over a new contract, left the Leicester boss purring at his scoring prowess following the 4-1 home win on Saturday.
King`s first was an exquisite chip over Tykes keeper Luke Steele, and his second was a clinical finish into the bottom corner from the edge of the box.
"He is a fantastic player and a fantastic captain," said Eriksson. "His finish for the first goal was top-class. You have to be very clever and have extremely good technique to score those goals.
"I have not set Andy any targets but I hope he keeps on scoring. But, of course, scoring that many goals as a midfielder is fantastic."